Wireworld Project

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Wireworld is a Cellular automaton with few simples rules but that is Turing-complete and that allow to simulate electornic logic elements. You can find more details on its Wireworld wikipedia page

Vocabulary

• Generation : iteration number of automaton. First generation is generation 0.
• Period : in case of repetitive thing period define the number of generation needed to come back in the same stategenerations necessaires pour revenir au meme etat
• n microns technology : n is the period between 2 electrons in an electron burst

Simulators

I wrote my own simulators for Wireworld automaton :

• A version whose simulator core is C++ based : Repo
• A version whose simulator core is [1] based : Repo

I use additional libraries like lib SDL 1.2 for graphical display and xmlParser for XML file parsing

Ressources sharing

Everything that is independant from simulator's core is located in a common package containing:

• Parser used to read automaton description
• Analyser which compute design partition and neigborhood to determine parts that will be simulated
• Generic configuration XML parser that allow design parametrisation
• Configuration parser which define design parameters

File formats

Input file

Automaton is described in a text file where each cell is represented by a character:

• . : empty cell
• # : copper cell
• E : electron head cell
• Q : electron tail cell

By example :

......................................................................#.......#.#........................................
......................................................................#.......#.#........................................
......................................................................#........##........................................
......................................................................#.........#........................................
...#################..###.......###.......###.....#.###.......###.....#.###.....#.###.......###.......###.......###......
..E.................###.##.##.###.##.##.###.##.##.###.##.##.###.##.##.###.##.##.###.##.##.###.##.##.###.##.##.###.##.##..
...Q################..#.#.#..#..#.#.#..#..#.#.#..#..#.#.#..#..#.#.#..#..#.#.#..#..#.#.#..#..#.#.#..#..#.#.#..#..#.#.#....
......................###.#.###.###.#.###.###.#.###.###.#.###.###.#.###.###.#.###.###.#.###.###.#.###.###.#.###.###.#....
.......................#..#..#...#..#..#...#..#..#...#..#..#...#..#..#...#..#..#...#..#..#...#..#..#...#..#..#...#..#....
.......................#.#.#.#...#.#.#.#...#.#.#.#...#.#.#.#...#.#.#.#...#.#.#.#...#.#.#.#...#.#.#.#...#.#.#.#...#.#.#...
.......................#.#.#.#...#.#.#.#...#.#.#.#...#.#.#.#...#.#.#.#...#.#.#.#...#.#.#.#...#.#.#.#...#.#.#.#...#.#.#...
........................#..#.#....#..#.#....#..#.#....#..#.#....#..#.#....#..#.#....#..#.#....#..#.#....#..#.#....#..#.#.
..........................#..#......#..#......#..#......#..#......#..#......#..#......#..#......#..#......#..#......#..#.
..........................#..#......#..#......#..#......#..#......#..#......#..#......#..#......#..#......#..#......#..#.
..........................#..#......#..#......#..#......#..#......#..#......#..#......#..#......#..#......#..#......#..#.
...........................##........##........##........##........##........##........##........##........##........##..

Generic configuration file

The file format is XML and it defines items associated to cell coordinates that will be electron head or tail.
Coordinates defined in items are relative to coordinates defined at the beginning of file.
When an item is configured then associated cells will be electron head or tail, else it initial state will be the one defined in input file

<?xml version="1.0" encoding="UTF-8"?>
<generic_definition version ="1.0">
  <origin coord="178,182"/>
  <item_list>
    <item name="init_pulse_1" e_head="-8,11"/>
    <item name="init_pulse_2" e_tail="-15,11"/>
    <item name="shift_1" e_head="-167,13" e_tail="-168,13"/>
    <item name="shift_2" e_head="-173,13" e_tail="-174,12"/>
  </item_list>
</generic_definition>

Configuration file

It complete the generic configuration file by defining if items are active or not.
File format is basic : item_name:[0|1]
Here is an example :

# Test file
init_pulse_1:1
init_pulse_2:1
shift_1:0
shift_2:1
#EOF

SystemC simulator

Each automaton's cell is represented by a SystemC module containing

• An input boolean port for clock signal
• An array of input boolean port whose size depends on neighbor number
• A boolean output port indicating if cell is in electron head state

SystemC module contains a SystemC process sensitive on clock that will do the following depending on cell's interal state:

• Count number of boolean inputs whose value is 1
• Update cell's internal state
• Update boolean output depending on cell's internal state

Output of neighbor cells are bound to cell's inputs.
In order to improve performances, SystemC module is templated on number of neighbor cells and the correct module type is instanciated by analyzer depending on neighbor number.

Wireworld Computer Reverse Engineering

Wireworld computer is a design based on wireworld cellular automaton. It defines an URISC processor with TTA architecture containing 64 registers of 16 bits
This design has been realised between 1990 and 1992 by David Moore, Mark Owen and some other people and can be considered as a precursor of what some people do today with Minecraft and its Redstone extension
A Turing Machine based on Game of life had been designed several years before Wireworld Computer but is programming was far les suser friendly compared to the one of wireworld computer
When a discovered this design and saw it simulated I was immediately fascinated. The web site explain its global operating but major part of the design is not explain in details so I was interested in understanding the following points:

• how the design operate
• how complexity emerge from very few simple rules
• how authors succeeeded to overcome difficulties raised by this automaton: propagation constraints, spatial constraints due to 2D universe etc

Before reading the following it is interesting to read the few pages of wireworld computer website to understand general operating principles of Wireworld computer

Methodology

• I use my C++ simulator to run the design in performance mode
• I use my SystemC simulator to run the desing in debug mode :
  • Evolution of automaton cell states is recorded in VCD format
  • I use GTKwave to open them
• For some part of the design I use Logisim to simulate them as logic gates. It allows to have a more 'understandable' view

Clock system

A simple way to generate a period P clocks is to draw a loop with size P containing a single electron.
This approach works well for small values of P but become space exepensive with huge values.
The clock system address this issue with a compact and elegant design that allow to geerate clocks with large periods in a size-contained space

It is composed of

• A clock injector
• A chain of clock dividers

Clock injector

This is a simple loop with inject an electron in clock dividers chain with a period of 36
In the remaining part of Wireworld Computer reverse engineering the leftmost copper cell will be considered as time origin and coordinates origin for the other cells

Clock divider

It allows to divide clock frequency by 2.
It is composed of 2 logic gates ( XOR and A & /B ), a loop and a delay path.
The loop is used as electron generator and has period of 12.
36 being a multiple of 12 and the loop being powered by clock injector, when the loop will be full an electron will arrive on the XOR gate at the same time than an electron coming from clock injector
An electron spend 4 generations to go from cell common to loop and delay path to A input of gate A & /B
An electron spend 16 générations to go from cell common to loop and delay path to B input of gate A & /B
It means the delay is 12 générations which is the period of the loop so nth electron will arrive on A & /B gate at the same time than electron (n - 1)th. Only the first electron will arrive alone on the gate and will succeed to go ahead
In schematic below loop period and delay path are modelledf by a D flip-flop.

• At startup loop is empty. The first arriving electron will fill it. Thanks to delay introduced by the delay path the first electron go through gate A &/B but not the following electron.
  
• The next electron that will arrive on XOR gate will empty the loop but will not reach the output due to the lock of A& /B gate
  

By this way only one electron of two reach the output of clock divider

Implemented feature

Clock injector period being 36 and each clock divider dividing clock frequency by 2 ( ie multiplying period by 2 ) the clock system allow to generate in a compact design several clock frequencies.
it is composed of 10 clock dividers and has outputs after 5h and 6h division unit which allows to have respective output frenquencies :

• After clock divider 5 : 36 * 2^5 = 36 * 32 = 1152
• After clock divider 6 : 36 * 2^6 = 36 * 64 = 1152 *2 = 2304

Digit display

Display of numbers in Wireworld Computer is realised by 5 digits displays
Each digit display is composed of :

• 1 7 segments display
• 1 ROM with 10 inputs and 7 outputd
• 1 ROM controller

7 segments display

It consist of wireworld cells assembled to represent a 7 segments display
Each segment is supplied by a wire that is distributed between several wires
Wires filled with electrons represent enlighted segments.
To maximise the "shine" of a wire electrons must be very closed each other wich consist of using 3 microns technology which is the thinnest allowed by Wireworld The other parts of digit display are designed in 6 microns technology so each input of 7 segments display has a frequency doubler:

• Each incoming electron ( period 6 ) is duplicated and delay of 3 generations before being reintroduced in an OR gate which generates 2 electronds with period 3

ROM

It codes the correspondancy between a digit and its represention on 7 segments display
Its operating is not the same than standard ROM. Indeed in a standard rom inputs biary code the address of the ROM that has to be read.
In this case each correspond to a single address so there are as much address as inputs which means that only one input should be active at a time : input n code for digit n.
For one electron coming on a ROM input, one electron will be generated on each ouput of the ROM coding 1.
To maintain segments lighted the ROM input correspoding to the digit must be continuously supplied.
This feature is implemented by ROM controller

ROM model

For this component electron propagation time is not meaningfull functionnally so they are not modelled. The ROM is partially modelled: only digits 0 to 6 are managed

• In a first time circuit is empty, an electron is supplied to light the zero
• At each cycle the active column/input will be shifted to light up next digit

Contrôleur de ROM

Its role is to continuously supply ROM and to select whcih ROM input will be supplied with electrons

Each ROM input is bound to a 6 period loop going through an OR gate, to introduce an electron in the loop, and an A & /B gate, to empty the loop.
Each input loops are bound in the following way :

• A wire going out from loop n-1 go into A input of A & /B gate, controlling loop transfer, while output of this gate is bound to input of OR gate responsible of electon introduction in loop n
• A wire going out from loop n + 1 go into B input of A & /B gate controlling the loop n clean

By this way in case loop n is supplied and B input of n to n+1 transfer gate is supplied than n remain active.
In case input B is no more supplied than electron of loop n will be duplicated in loop n+1 which will clean loop n.
Thanks to this mechanism there is only one loop active at at time so there is only one ROM input active at a time.

B inputs of transfer gates are all bound on the same wire itself bound on on a A & /B gate output whose A input is driven by an electron generator of period 6.
By controling B input it is possible to stop the supply of transfer gates.
A loop transfer needs 10 generations to be performed so for each electron locked the active input of ROM is shifted by one.

Remark:

• To make the ROM controller work properly the electron stored in the loop need to arrive on transfer gate input at the same time than electron produced by electorn generator
  
• There is a 10th loop that allow to clean the 9th loop
  
• The logic gate OR controllinh the electron introduction in loop 0 is supplied by a wire going through a "tailer", a logic gate of type n & !(n+1) for 6 microns technology, which means that if n electrons arrive only ce qui signifie qui si l on envoie n electrons, only the n-1eme will go through the gate.
  

Operating

• In case 10 electrons are sent on this wire and on loop transfer control wire then then 10 loops bound on ROM inputd are clean and one electron is introduced in loop 0 meaning that 0 wil be displayd on 7 segments display.
• If we want to display 5 and the displayed digit is zerp then it is needed to send 5 electrons on loop transfer control wire to activate loop 5

ROM controller model

In this example D flip-flop are there only to model electrons' propagation delay
Only loop 0 to 3 and clean loop have been modelled
To keep a reasonable model's size I use a standard ROM where only addresse having only one bit at 1 are used

• In a first time circuit is empty, an electron is introduced to display 0
• After few cycles 3 electrons are sent on B input to display 3
• After few cycles a burst of electron is sent to clean loops and reset display

Data latch

This module control :

• When data coming from register 0 is tkane in account and sent to binary/BCD converter
• Reset of digit display

Inputs/Outputs

Tt has 3 inputs:

• Data coming from register 0 ( picture bottom left)
• Write command indicating that a new value has been written in register 0 (picture bottom right)
• Set command to indicate that data should be loaded in adder of binary/BCD converter (picture top right)

The Set command is sent by bottom megaloop of binary/BCD converter

It has 2 outputs:

• Digit display reset that will make all 7 segments displays display zero ( picture top left )
• Data to load in adder of binary/BCD converter (picture top center )

Internal architecture

It is made up of :

• 3 microns clock always active (C1) + 1 transistor (Tf)
• 6 microns clock with set and reset (C2)
• 6 microns clock de 6 microns always active (C3)
• 3 transistors (T1,T2,T3)
• 3 XOR gates to implement a wire crossing
• 1 path that can contain 16 electrons in 6-microns
• 1 "header" for 6 microns burst that allow only first electron to go through

Operating

Bottom megaloop of Binary/BCD converter, bound to Set input of Data Latch, contains an electron that is the Set command and a list of aritmetic values in 6 microns.
These values should not generate Set command so they must be filtered
Filetering is done by the 3 microns clock C1 which drives a transistor Tf controlling if electron coming from Megaloop continue in Data latch or not.
Arithmetic values of megaloop are coded in 6 microns and are in phase which C1 meaning that each electron of arithmetic value reach transistor Tf input at the time electron generated by clock C1 disable transistor Tf so megaloop electrons don't go throught transistor
Command electron is slightly out of phase compared to clock C1 which allows it to go trough Tf and to generate Set command.

Set command trigger the introduction of an electron inside the loop of clock C2 that will generate burt of electron flow with a 6 microns period.
The Write command empty this loop.
This command is made up of 16 electrons in 6 microns but only the first one has an effect, indeed the following electrons will empty an already empty loop.
The electron flow generated by C2 clock go along 2 different wires :

• A wire going to transistor T1 input and then on control input of transistor T2
• A central wire that can contain 16 electrons in 6 microns and that go into control input of transistor T1

The central wire cross the Data input wire thanks to 3 XOR gates and supply too a header that will only let the first electron go to Reset output controlling digit display reset

When central wire is full than its electrons disable T1 transistor so electrons coming from clock C2 cannot pass.
These electrons disable T2 transistor which prevents electrons coming from clock C3 to reach transistor T3 control input
Transistor T3 control transfer from Data input to Data output

• During normal operating:
  • C2 clock is active and central wire is full
  • T1 transistor is disabled so electrons from C2 cannot reach control input of T2 transistor
  • T2 transistor is enabled so electrons from C3 reach control input of transistor T3
  • T3 transistor is disable so Data input cannot go to Data output.

• When Write command arrive:
  • Loop of clock C2 become empty. There are no more electrons sent to central wire
  • Central wire become empty
  • T1 become enable but C2 loop is empty so no electron go through T1 so T2 remains enabled
  • Transistor T3 remains disabled so Data input cannot go to Data output.

• When Set command arrive:
  • An electron is introduced C2 loop which restart to generate electrons every 6 microns
  • Central wire is filling
  • Until central wire is full T1 remains enabled so the first 16 1er electrons coming from C2 reach T2 control input
  • T2 is disabled by par 16 consecutive electrons so 16 electrons from C3 clock doesn't reach control input of T3
  • T3 is enabled and let the 16 electrons go from Data input to Data output

Once central path is full operating come back to normal mode

Remark :In order Data Latch work properly the following timing constraints must been respected:

• Write command should be synchronised with C2 loop to empty it
• Set command should arrive with the good timing so that Data 16 electrons arrive on T3 input when it is enabled

Binary/BCD converter

Kind reminder, BCD is a way to code decimal representation of binary numbers using 4 bits to represent each digit
By example, BCD representation of 125 is 0001 0010 0101.

The Binary/BCD converter is one of the most complex part of Wireworld Computer, which is reflexed by the number of cells and the area it represents in the full design.

Inputs/Outputs

Binary/BCD converters has 1 input and 5 outputs
Its input receive binary data coded on 16 bits LSB first The 5 outputs are :

• a pair of wire for each digit display

Internal architecture

Binary/BCD converter is composed of several parts:

• Binary adder
• Digit selecter
• Overflow detection loop associated to a pulse generator
• Pulse controler for digit display
• 2 mega loops

Binary adder

This is a standard serial binary adder whose output is bound on one of its input.
Loop period is 193 générations which allow him to operate on numbers coded on 32 bits in 6 microns.

Digit selecter

Inputs/Outputs

It has 2 inputs:

• reset input driven by Digit display reset output coming from Data Latch
• Digit change input driven by pulse controler for digit display
• Data input which receive pulses send by pulse generator and destinated to digit displays

and 5 outputs:

• One output, made up a pair of wire, per digit display

Internal architecture

The way its control part operates is very similar to the way displays's controler is working

• It is made up of a series of 5 electron generation loops with a set and a reset that are bound each other
  
• Digit_display[n] is driven by loop[n], Digit_display[0] control unit digit
  
• loop[n+1] drive reset of loop[n] so that if loop[n+1] is active then reset command of loop boucle[n] is intercepted
• Every set are driven by the Digit change input

The loop outputs are bound on transistors controlling replication of B input of double A AND NOT gates to their A input
These logic gates have 2 outputs S1 and S2 respectively bound to control input of digit display and to B input of next gate. The outputs implement the following equations:

• S1 = /A && B
• S2 = B && /A

gate[0] has its B input bound to pulse generator output while gates[n] have their B input boudn to S2 output of gate[n-1]
By this way when loop[n] is active it locks transistor[n] so gate[n] has its A input at 0 so S2 = B making electrons coming from pulse generator go to gate[n+1]
On the other hand when loop[n] is empty then transistor[n] is enable so electron coming from pulse generator is replicated on B input.
Due to propagation delay A went down to 0 making S1 change to 1 so electron is send to digit display

Operating

• By default all loops are active
• When Data Latch send its reset it makes loop[4] empty
• When pulse controller send a digit change command then as loop correspondig to active digit display[n] is empty then reset of loop[n-1] is not intercepted so loop[n-1] while loop[n] is refilled
• When loop[0] is reactivated then other loops are active too so we come back to default state

Overflow detection loop and pulse generator

The period of this loop is 193, it stores one electron and is synchronised with the binary adder loop
The electron control activation of set and reset of a period 6 loop ( gen loop ) in pulse generator:

• If there is no overflow in binary adder then reset is done just after set no pulse is generated
• If there is an overflow in adder than transistor is disabled which inhibit reset so pulses are generated by period 6 loop

Due to the length of the overflow detection loop the pulse generator produce 32 electrons pulses before loop 6 period reset is performed by detection loop

Pulse controller

It has 1 input:

• It receives pulses sent by pulse generator

and 2 outputs :

• Pulse output that will send only pulses needed to display the correct digit
• Digit change that will emit an electro to indicate to digit selector that it should select an other digit

Pulse controller is mainly made up of a loop with period 769 which allow it to store 4 values coded on 32 bits in 6 microns
Values stored in pulse controller loop:

Index	Hexadecimal value	Binary value	Number of bits with value 0
0	0x7FFFFFFF	0111 1111 1111 1111 1111 1111 1111 1111	1
1	0x77777777	0111 0111 0111 0111 0111 0111 0111 0111	8
2	0x7F7F7F7F	0111 1111 0111 1111 0111 1111 0111 1111	4
3	0x7FFF7FFF	0111 1111 1111 1111 0111 1111 1111 1111	2

In addition to these values pulse controller loop contain an out-of-phase electron
On the top-left part of pulse controller there is a transistor Tn driven by a clock C3 of période 3 microns which filters electrons coding values in the loop and prevent them to be sent on output wire driving digit change
On the other hand out-of-phase electron is not filtered and is able to go on output wire which allow to indicate to digit selecter to select an other digit
To work properply the pulse controler need to be well synchronised with pulse generator so that generated pulses for the current digit go through digit selecter before digit change command
Values stored in the loop are synchronised in such a way that they control Tc located at bottom-right wihich allow to control if pulses sent by pulse generator reach the output or not

• If value bit is 1 then Tc is locked and electron sent by pulse generator does not reach output.
• If value bit is 0 then Tc is unlocked and electron sent by pulse generator reach output.

Mega loops

Mega loops are huge size circular buffers containing some numeric values.
Their period is 3841 générations which allow them to store 640 bits which represents 20 values coded on 32 bits in 6 microns
Compared to electron move direction in the loop values are stored LSB first

Values stored in megaloop:

Index	Top Megaloop	Bottom Megaloop
0	0xFFFFFF80	0xFFFF63C0
1	0x0	0x4E20
2	0x0	0x2710
3	0x1890	0x7D0
4	0x0	0xFA0
5	0x0	0x7D0
6	0x0	0x3E8
7	0x3E8	0xC8
8	0x0	0x190
9	0x0	0xC8
10	0x0	0x64
11	0x44	0x14
12	0x0	0x28
13	0x0	0x14
14	0x0	0xA
15	0xA	0x2
16	0x0	0x4
17	0x0	0x2
18	0x0	0x1
19	0x1	0x1

Bottom megaloop contains too an out-of-phase electron compared to values electrons.
This is this particular electron that will not be filtered by transistor Tf of data latch and that will be the Set command
Electrons coding values are in phase with Tf lock and will be filtered

Operating

Principle

Base principle of Binary/BCD converter is overflow detection
The value to be displayed will be added with a series of predefined values stored in bottom megaloop which generate or not some overflows
When an overflow is detected then pulse generator is activated and generates pulses composed of 32 electrons
These electrons go on input of a transistor drivent by pulse controller
Depending on current value of pulse controler at this time only 1,2,4 ou 8 electrons will succeed to pass through the transistor and reach data input of digit selecter that will route them to the correct digit display
To display a digit d you need to decompose it in a sum of 1, 2 4, 8 which is equivalent to code it in binary
As we are in base ten to display a number n with need to decompose it in a sum of (1, 2 4, 8) * 10 exponent(digit_position)

Remark : The 32 electrons burst generated in case of overflow is re-injected in adder carry to disable it. Values contained in top megaloop are computed in a way that prevent carry to propagate between 2 decimal digits that's why we can remark that megaloop values are not null for indexes corresponding to stronger bit of each digit coded in BCD

Arithmetic

Operations performed in Binary/BCD converter are done on 32 bits, consequently the maximum representable value is 0xFFFFFFFF
If first bottom megaloop value is substracted to this maximum value the result is the following :

• 0xFFFFFFFF - 0xFFFF63C0 = 39999

meaning that every number >= 40000 added to 0xFFFF63C0 will generate an overflow. By repeating this process on other values of bottom megaloop we obtain the following array :

Index	Previous value	Current value	V[n-1] + V[n]	Substraction from Vmax	Overflow limit
0	0xFFFF63C0	0x4E20	0xFFFFB1E0	0xFFFFFFFF – 0xFFFFB1E0	19999
1	0xFFFFB1E0	0x2710	0xFFFFD8F0	0xFFFFFFFF – 0xFFFFD8F0	9999
2	0xFFFFD8F0	0x7D0	0xFFFFE0C0	0xFFFFFFFF – 0xFFFFE0C0	7999
3	0xFFFFE0C0	0xFA0	0xFFFFF060	0xFFFFFFFF – 0xFFFFF060	3999
4	0xFFFFF060	0x7D0	0xFFFFF830	0xFFFFFFFF – 0xFFFFF830	1999
5	0xFFFFF830	0x3E8	0xFFFFFC18	0xFFFFFFFF – 0xFFFFFC18	999
6	0xFFFFFC18	0xC8	0xFFFFFCE0	0xFFFFFFFF – 0xFFFFFCE0	799
7	0xFFFFFCE0	0x190	0xFFFFFE70	0xFFFFFFFF – 0xFFFFFE70	399
8	0xFFFFFE70	0xC8	0xFFFFFF38	0xFFFFFFFF – 0xFFFFFF38	199
9	0xFFFFFF38	0x64	0xFFFFFF9C	0xFFFFFFFF – 0xFFFFFF9C	99
10	0xFFFFFF9C	0x14	0xFFFFFFB0	0xFFFFFFFF – 0xFFFFFFB0	79
11	0xFFFFFFB0	0x28	0xFFFFFFD8	0xFFFFFFFF - 0xFFFFFFD8	39
12	0xFFFFFFD8	0x14	0xFFFFFFEC	0xFFFFFFFF – 0xFFFFFFEC	19
13	0xFFFFFFEC	0xA	0xFFFFFFF6	0xFFFFFFFF – 0xFFFFFFF6	9
14	0xFFFFFFF6	0x2	0xFFFFFFF8	0xFFFFFFFF – 0xFFFFFFF8	7
15	0xFFFFFFF8	0x4	0xFFFFFFFC	0xFFFFFFFF – 0xFFFFFFFC	3
16	0xFFFFFFFC	0x2	0xFFFFFFFE	0xFFFFFFFF – 0xFFFFFFFE	1
17	0xFFFFFFFE	0x1	0xFFFFFFFF
18	0xFFFFFFFF	0x1	0

It is obvious that overflow limits correspond to code with 1,2,4,8 and 10 powers

Simulation

C++ code below implement arithmetic principle of Binary/BCD converter and display internal states to illustate its operating

#include <iostream>
#include <stdint.h>
#include <stdlib.h>
#include <iomanip>

using namespace std;

int main(int argc, char ** argv)
{
  if(argc != 2)
    {
      cout << "Usage is binary2bcd <number>" << endl ;
      exit(-1);
    }
  uint64_t l_number = strtoll(argv[1],NULL,0);
  cout << "Input number is " << l_number << endl ;

  uint32_t l_bottom_loop[] = {
    0xFFFF63C0,
    0x4E20,
    0x2710,
    0x7D0,
    0xFA0,
    0x7D0,
    0x3E8,
    0xC8,
    0x190,
    0xC8,
    0x64,
    0x14,
    0x28,
    0x14,
    0xA,
    0x2,
    0x4,
    0x2,
    0x1,
    0x1
  };

  uint32_t l_top_loop[] = {
    0xFFFFFF80,
    0x0,
    0x0,
    0x1890,
    0x0,
    0x0,
    0x0,
    0x3E8,
    0x0,
    0x0,
    0x0,
    0x44,
    0x0,
    0x0,
    0x0,
    0xA,
    0x0,
    0x0,
    0x0,
    0x1,
  };

  uint64_t l_adder_content = l_number;
  uint64_t l_adder_full = 0xFFFFFFFF;
  uint32_t l_display[5] = {0,0,0,0,0};
  uint32_t l_display_index = 0;
  uint32_t l_power_index = 2;
  uint32_t l_carry = 0;
  
  //std::cout << "carry : 0x" << setw(8) << setfill('0') << hex << l_carry << dec << endl ;
  for(uint32_t l_index = 0; l_index < 20 ; ++l_index)
    {
      if(((l_index + 1) % 4) == 0)
	{
	  std::cout << "-------------------------------------------------------";
	  std::cout << "-------------------------------------------------------";
	  std::cout << "-------------------------------------------------------";
	  std::cout << "--------------------------------------------------" << std::endl ;
	}
      std::cout << "Step[" << setfill(' ') << setw(2) << l_index << "]: ";
      cout << "carry : 0x" << setw(8) << setfill('0') << hex << l_carry << dec << " & ~(" ;
      cout << "Top_loop[" << setfill(' ') << setw(2) << l_index << "] : 0x" << setw(8) << setfill('0') << hex << l_top_loop[l_index] << dec << ") => " ; 
      l_carry = l_carry & ( ~ (l_top_loop[l_index]));
      cout << "Adjusted carry 0x" << setw(8) << setfill('0') << hex << l_carry << dec << " ^ " ;
      cout << "Bot_loop[" << setfill(' ') << setw(2) << l_index << "] : 0x" << setw(8) << setfill('0') << hex << l_bottom_loop[l_index] << dec << " => " ; 
      uint32_t l_to_add = l_carry ^ l_bottom_loop[l_index];
      cout << "To add 0x" << setw(8) << setfill('0') << hex << l_to_add <<dec << " + " ;
      cout << "Adder content : " << setw(8) << setfill('0') << hex << l_adder_content << dec << " | " ;
      l_adder_content +=  l_to_add;
      cout << "==> Adder content : " << setw(8) << setfill('0') << hex << l_adder_content << dec ;
      if(l_adder_content > l_adder_full)
	{
	  cout << "\tOverflow !" ;
	  l_adder_content = (l_adder_content & 0xFFFFFFFF) + 1;
	  l_carry = 0xFFFFFFFF;

	  // Part implemented by Pulse controler
	  l_display[l_display_index]+= 1 << l_power_index;
	}
      else
	{
	  l_carry = 0;
	}
      // Part implemented by Pulse controler
      l_power_index = (l_power_index > 0 ? l_power_index - 1 : 3);
      // Part implemented by Pulse controler and Digit display controler
      if(l_power_index == 3)
	{
	  ++l_display_index;
	}
      cout << endl;
    }

  // Display Results
  for(uint32_t l_index = 0 ; l_index < 5; ++l_index)
    {
      cout << "|" << l_display[l_index] ;
    }
  cout << "|" << endl ;
}

To compile it use the following command

g++ -Wall -ansi -pedantic -g -std=c++11 -D__STDC_FORMAT_MACROS -D__STDC_LIMIT_MACROS -D__STDC_CONSTANT_MACROS binary2bcd.cpp -o binary2bcd.exe

Here is an execution example:

$ ./binary2bcd.exe 0x100
Input number is 256
Step[ 0]: carry : 0x00000000 & ~(Top_loop[ 0] : 0xffffff80) => Adjusted carry 0x00000000 ^ Bot_loop[ 0] : 0xffff63c0 => To add 0xffff63c0 + Adder content : 00000100 | ==> Adder content : ffff64c0
Step[ 1]: carry : 0x00000000 & ~(Top_loop[ 1] : 0x00000000) => Adjusted carry 0x00000000 ^ Bot_loop[ 1] : 0x00004e20 => To add 0x00004e20 + Adder content : ffff64c0 | ==> Adder content : ffffb2e0
Step[ 2]: carry : 0x00000000 & ~(Top_loop[ 2] : 0x00000000) => Adjusted carry 0x00000000 ^ Bot_loop[ 2] : 0x00002710 => To add 0x00002710 + Adder content : ffffb2e0 | ==> Adder content : ffffd9f0
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Step[ 3]: carry : 0x00000000 & ~(Top_loop[ 3] : 0x00001890) => Adjusted carry 0x00000000 ^ Bot_loop[ 3] : 0x000007d0 => To add 0x000007d0 + Adder content : ffffd9f0 | ==> Adder content : ffffe1c0
Step[ 4]: carry : 0x00000000 & ~(Top_loop[ 4] : 0x00000000) => Adjusted carry 0x00000000 ^ Bot_loop[ 4] : 0x00000fa0 => To add 0x00000fa0 + Adder content : ffffe1c0 | ==> Adder content : fffff160
Step[ 5]: carry : 0x00000000 & ~(Top_loop[ 5] : 0x00000000) => Adjusted carry 0x00000000 ^ Bot_loop[ 5] : 0x000007d0 => To add 0x000007d0 + Adder content : fffff160 | ==> Adder content : fffff930
Step[ 6]: carry : 0x00000000 & ~(Top_loop[ 6] : 0x00000000) => Adjusted carry 0x00000000 ^ Bot_loop[ 6] : 0x000003e8 => To add 0x000003e8 + Adder content : fffff930 | ==> Adder content : fffffd18
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Step[ 7]: carry : 0x00000000 & ~(Top_loop[ 7] : 0x000003e8) => Adjusted carry 0x00000000 ^ Bot_loop[ 7] : 0x000000c8 => To add 0x000000c8 + Adder content : fffffd18 | ==> Adder content : fffffde0
Step[ 8]: carry : 0x00000000 & ~(Top_loop[ 8] : 0x00000000) => Adjusted carry 0x00000000 ^ Bot_loop[ 8] : 0x00000190 => To add 0x00000190 + Adder content : fffffde0 | ==> Adder content : ffffff70
Step[ 9]: carry : 0x00000000 & ~(Top_loop[ 9] : 0x00000000) => Adjusted carry 0x00000000 ^ Bot_loop[ 9] : 0x000000c8 => To add 0x000000c8 + Adder content : ffffff70 | ==> Adder content : 100000038    Overflow !
Step[10]: carry : 0xffffffff & ~(Top_loop[10] : 0x00000000) => Adjusted carry 0xffffffff ^ Bot_loop[10] : 0x00000064 => To add 0xffffff9b + Adder content : 00000039 | ==> Adder content : ffffffd4
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Step[11]: carry : 0x00000000 & ~(Top_loop[11] : 0x00000044) => Adjusted carry 0x00000000 ^ Bot_loop[11] : 0x00000014 => To add 0x00000014 + Adder content : ffffffd4 | ==> Adder content : ffffffe8
Step[12]: carry : 0x00000000 & ~(Top_loop[12] : 0x00000000) => Adjusted carry 0x00000000 ^ Bot_loop[12] : 0x00000028 => To add 0x00000028 + Adder content : ffffffe8 | ==> Adder content : 100000010    Overflow !
Step[13]: carry : 0xffffffff & ~(Top_loop[13] : 0x00000000) => Adjusted carry 0xffffffff ^ Bot_loop[13] : 0x00000014 => To add 0xffffffeb + Adder content : 00000011 | ==> Adder content : fffffffc
Step[14]: carry : 0x00000000 & ~(Top_loop[14] : 0x00000000) => Adjusted carry 0x00000000 ^ Bot_loop[14] : 0x0000000a => To add 0x0000000a + Adder content : fffffffc | ==> Adder content : 100000006    Overflow !
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Step[15]: carry : 0xffffffff & ~(Top_loop[15] : 0x0000000a) => Adjusted carry 0xfffffff5 ^ Bot_loop[15] : 0x00000002 => To add 0xfffffff7 + Adder content : 00000007 | ==> Adder content : fffffffe
Step[16]: carry : 0x00000000 & ~(Top_loop[16] : 0x00000000) => Adjusted carry 0x00000000 ^ Bot_loop[16] : 0x00000004 => To add 0x00000004 + Adder content : fffffffe | ==> Adder content : 100000002    Overflow !
Step[17]: carry : 0xffffffff & ~(Top_loop[17] : 0x00000000) => Adjusted carry 0xffffffff ^ Bot_loop[17] : 0x00000002 => To add 0xfffffffd + Adder content : 00000003 | ==> Adder content : 100000000    Overflow !
Step[18]: carry : 0xffffffff & ~(Top_loop[18] : 0x00000000) => Adjusted carry 0xffffffff ^ Bot_loop[18] : 0x00000001 => To add 0xfffffffe + Adder content : 00000001 | ==> Adder content : ffffffff
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Step[19]: carry : 0x00000000 & ~(Top_loop[19] : 0x00000001) => Adjusted carry 0x00000000 ^ Bot_loop[19] : 0x00000001 => To add 0x00000001 + Adder content : ffffffff | ==> Adder content : 100000000    Overflow !
|0|0|2|5|6|

The Overflow represent bits with 1 value in BCD code with first bit being the MSB

Registers access controller

Wireworld Computer contains 64 registers 16 bits width, registers access controllers allow to select register to write in or to read from
There is a write access controller and a read access controller
Register selection is done by sending two burst of 16 electrons in 6 microns, one burst going in direction of register bank top and one going in direction of register bank bottom.
Register located at point where the tow burst will met up become reachable.
The falling burst is emitted with a fix period whereas the rising burst is emitted with a controllable delay
Controlling this delay allow to control the location where the 2 bursts will met up and consequently the accessed register.
The register access controller generate the rising burst with a delay depending on Id of registers that needed to be accessed.

Inputs/Outputs

Register access controllers have 2 inputs and 2 outputs.
The 2 inputs are the following:

• Access command that will activate controller
• Data containing Id of register we want to access to

The outputs are the following:

• Burst of 16 electrons in 6 microns generated with a fixed delay after access command
• Burst of 16 electrons in 6 microns generated with a variable delay after access command depending on register Id

Internal architecture

Each access controller is made up of the following elements:

• 2 burst generators of 16 electrons 6 microns : GSup and GSdown'
• 1 burst generator of 8 electrons 6 microns
• 1 electron doubler in 6 microns
• 2 delay generators in 6 microns
• 1 header that let pass only first electron of a burst

Burst generator of n electrons in 6 microns

They receive an electron as input and generate electron burst as output.
Operating principle is always the same :

• An electron activate a loop whose period is 6 microns
• Electrons generated by the loop go to the output and a feedback wire that control the reste of the period 6 loop.

The length of feedback wire determine how many electrons will be emitted before the first one make the loop empty.

Electron doubler in 6 microns

Electron coming at input is sent on 2 wires going on a OR gate
One wire is longer by 6 micron compared to the other which make that the output will receive one electron + one electron 6 generation later

Described using algorithm we obtain the following code for n=8:

// this code start to be executed at activation
bool B = true;
bool Bc[8]
do
{
  for(int I = 0 ; i < 8 ; ++i)
  {
    bool output_bit = B ^ Bc[I];
    if(Bc[I] == true)
    {
      B = false;
    }
    B[I] = output_bit
  }
} while(!B)
// Send electron to output

If we apply this code to a numeric value like 0011011 (LSB first) so 108

Index	0	1	2	3	4	5	6
Bc[Index] in input	0	0	1	1	0	1	1
B value	1	1	1	0	0	0	0
Bc[Index] in output	1	1	0	1	0	1	1

So an output value of 107 what was expected

Delay generator in 6 microns

They are chacterized by their period. Generated delay will be a multiple of their périod which is itself a multiple of 6 microns.
n is the factor ( périod / 6)
In input they receive:

• a value V coded on n bits
• a burst of n electrons considered as a value Vbis with n bits at 1

They generate the following outputs :

• a reference electron at time t
• an electron at time t` so thaht t` = t + constant + V * periode

Core of delay generator is a substracter working on values coded on n bits.
It is composed of :

• 2 loops: Ba the activation loop and Bc the computation loop. They have the same périod than generator and can store n bits
• a XOR gate
• 2 transistors T1 and T2
• A loop B of period 6 controllable (set/reset) which can store one bit
  

Activation electron is inserted in Ba which drive set of loop B.
Result of V AND Vbis is inserted in computation loop when delay generator is activated.
Bc go through XOR gate whose other input is the value contained in B.
B reset is directly bound to Bc so the first non zero bit in computation loop empty B
Ba is bound too to a wire in direction of output with a duplicator to transistor T1 which make it cancel itself unless B contains an electron in which case the duplicated activated electron doesn`t reach the input inhibiting transitor T1.
When substracter contains value zero, there are nore more bits at 1 to clean B so activation electron will reach the output and clean Ba via transistor T2. Output is generated by the substracter underflow

Operating principle

We saw that register controler contains 2 delay generators:

• One with a period 48 and so based on a 8 bits substracter: Gd48
• One with a period 12 and so based on a 2 bits substracter: Gd12

Both generators are chained so that output electron from period 48 generator activate period 12 generator
Command electron from register controler go inside electron doubler, the 2 generated electrons are sent:

• on Vbis input of Gd12 at the same time the 2 LSB electrons of register Id reach its V input
• on input of 8 electrons burst generator

The 8 electron burst is sent on Vbis input of Gd48 at the same time that the 6 MSB electrons of Register Id reach V input
The first of the 8 electrons is sent too on GSdown command while output of Gd12 command GSsup

The use of 2 generators delays with different periods allow to generate huge delays (Gd48) with a thin granularity of 12 generations (Gd12) which finally give a delay d between activation of GSup and GSdown defined as the following:

d = 48 * (RegisterId[7:2] >> 2) + 12 * RegisterId[1:0]

ignoring propagation constants

Control Unit

Operating principle

This the unit that drive the execution of Wireworld Computer by managing instruction cycle:

• Fetch(1/2) : Read Program Counter from Register[63]
• Fetch(2/2) : Read instruction MOV Rs Rt contained in Register[Program Counter]
• Decode(1/2) : copy value Rs on Register Id input of register read access controller
• Decode(2/2) : copy value Rt on Register Id input of register write access controller
• Execute(1/2) : Read value V contained in Register[Rs]
• Execute(2/2) : Write value V contained in Register[Rt]
• Incrementation of Program Counter to go to next instruction

To improve execution speed of Wireworld Computer all Fetch/Decode/Execute steps are done in parallel
By example step 1 of Fetch is done via a dedicated wire which allow to perform Execute(1/2) at the same time
Finally it leads to do 2 read operations for one write Operation
This is visible in the design by an output wire after 5th frewuency clock divier that command register read access controler and an output wire after register write access controler

The following array summarise ordering of the different operations

Operation 1	Operation 2	Operation 3	Read Register Id	Write Register Id	Data read	Data to write
Fetch(1/2)	Execute(1/2)	Decode(2/2)	PC value	Result from previous Fetch(2/2) = Rt	V = Content Register Rs
Fetch(2/2)	Execute(2/2)	Decode(1/2)	Rs		Instruction pointed by PC	V

Implementation

Inputs/Outputs

The control unit has the following inputs:

• Data D coming from register bank
• Program Counter value or PC
• Read command Cr
• Double electron from register read access controller
• Write command/PC read command

The control unit has the 2 following outputs:

• Read register Id
• Write Register Id/ Data to write

Internal architecture

Unit control is made up of the following elements:

• Incrementer
• XOR gate
• Double A AND NOT B L1 gate
• OR gate
• Transistor Tpc
• Triple XOR gate
• Transistor Tr
• Transistor Tw

Operating

Read command electron start a burst generator whose stop is driven by electrons generated by register read access controller electron doubler which generates a 16 electrons burst
Burst electrons go to the input of transistors Tr and Tw.
In case transistors are not locked burst electrons are sent:

• By Tr on Register Id input of register read access controler
• By Tw on Register Id input of register write access controler and on Data wire of register bank write side

The path of Data bus Data is very long so that Data arrives at register input at the it is activated by rising and falling burst of register write access as defined by Decode(2/2)'.
During Decode(1/2) value is on Data bus is not an instruction so timings are computed so that it arrives on Register Id input between 2 write command so it has no effects.
It was previously said that Tr and Tw are unlocked only when they are not driven so when sending a burst on input it means that Output = NOT Input control
During read operation on registers the output is NOT of register content and this result arrive on input control of Tw so the output of Tw is the value contained in register.
Read operation can be a register read or PC read in case of instruction fetch so there is some logics to manage both cases.
Write command electron is sent too to PC register
It starts PC incrementer and a burst generator that produce 8 electrons

PC/Data register selecter

Generated burst is sent to a XOR gate whose other input receive PC value.
XOR gate output so produce NOT(PC) which arrive on double A AND NOT B gate L1 whose other input receive PC. By this way both inputs never receive 1 at the same time so the gate behave as a wire cross and bottom output produce PC wherase top output produce NOT(PC).
NOT(PC) output is bound on the input of OR gate whose other input receive data coming from registers.
OR gate output is bound on transistor Tpc driven by PC value.

In case of simple register read XOR gate has input at 0 so its output is PC.
L1 gate perform AND NOT of PC and PC so output remains 0 so OR gate output is value coming from registers, as Tpc is not driven value go in direction of Tr transistor through wire crossing implemented by the triple XOR gate.

In case of PC fetch OR gate receive in input value coming from registers and NOT(PC).
Tpc transistor is driven by PC do transistor output is ((NOT(DATA)) OR (NOT(PC))) & NOT(PC).

• When PC bit is 1 output is zero
• When PC bit is zero output is NOT(Data) OR NOT(PC), as PC bit is zero OR output is 1. PC drives Tpc so transitor output is NOT(PC)

PC incrementer

PC value go throught incrementer XOR gate whose other input come from a period 6 loop Linc.
This loop is loaded by PC read command electron and the reset is driven by the output of a transistor Tr driven by PC bits and whose input is supplied by a period 6 clock L
If PC bit is at 1 then transistor Tr is locked so electron coming from clock L doesn't reset loop Linc and does not lock transistor To so electron emitted by L reach register output which allows to have PC value at register output despite incrementer logic
If PC bit is at 0 then transistor Tr is unlocked so electron coming from clock L reset loop Linc and lock transistor To so electron emitted by L does not reach register output which allows to have PC value at register output despite incrementer logic. Due to propagation delay Linc is clear only after value it contains has been XORed with PC bit so first PC bit with zero value is set to 1
From arithmetic point of view while PC bits are at 1 Linc keep value 1 so PC bits are XORed to zero, the first zero bit will be set to 1 while Linc will be empty so next bits will remain unchanged. This is an increment.

Described in algorithmic way we obtain the following code for n=4 wit n the number of bits coding PC value:

// this code start to be executed when reading PC
bool B = true;
// PC value
bool PC_in[8]
// PC value
bool PC_out[8]

for(int I = 0 ; i < 8 ; ++i)
{
    PC_out[I] = B ^PC_in[I];
    if(!PC_in[I])
    {
       B = false;
    }
}

If we apply this code to a numeric value like b00000000 (LSB first) so 0

Index	0	1	2	3	4	5	6
PC_in[Index]	0	0	0	0	0	0	0
B value	1	0	0	0	0	0	0
PC_out[Index]	1	0	0	0	0	0	0

So an output value of b10000000 (LSB first) so 1 what was expected

If we apply this code to a numeric value like 11100000 (LSB first) so 7

Index	0	1	2	3	4	5	6
PC_in[Index]	1	1	1	0	0	0	0
B value	1	1	1	1	0	0	0
PC_out[Index]	0	0	0	1	0	0	0

So an output value of 00010000 (LSB first) so 8 what was expected

Registers

There are 64 and are composed of:

• a loop of periode 96 used to store the data, a 16 bits word in 6 microns
• logic to write in register
• logic to read from register

Registers are serial registers meaning that they should written and read bit by bit

Register write

Operating principle

To write in a register it is needed to generate a write command and to present a data on register input
In wireworld computer data arrived from wire bound at register bank top right and will fall along register bank through a logic gate stream
Write command is generated at level of a single register and should be synchronised with the data so that they both arrive at the same time on register and data should be synchronised too with register loop so that first bit of data to be written is introduced in register at the location of the first bit stored in the loop
Write command will stop data propagation along bank register and will "deflect" it inside register
Write command is generated by register write access controller via 2 electron bursts

• One that raise along a wire located on the right of write logic mechanism
• One that fall between previous wire and data wire

So cells located in input of each register should implemnt the following features:

• Propagation of data to be written to bottom of register bank
• Propagation of rising and falling bursts along register bank
• Sending data to register selected by collision of rising and falling burst

Implementation

The write logic is composed of the following gates:

• 2 AND NOT gates called Lsel1 Lsel2
• 1 double AND NOT gate called X
• 2 AND NOT gates called 'Lndata1 Lndata2
• 1 OR gate

Detection of collision is performed thanks to logic gates Lsel1 et Lsel2 which implement the following function:

• f = (rising_burst AND NOT ( rising_burst AND NOT falling_burst))

By this way f value is 1 only when rising_burst and falling_burst are at 1 the same time which is the case during their collision

Gate X receive as input data to write and f, its bottom output is bound to top input of next register's X gate and income timings are computed in such a way that

• If f is 0 data to be writtend is propagated to the bottom of register bank
  
• If f is 1 data is not propagated to the bottom and top output of X is f'=f

Value contained in register go through OR gate via A input and f` is bound on B input so when register is selected previous value is replaced by a 16 electron burst, when register is not selected value remains the same.
During data propagation to bottom of register bank data arrive on B input of logic gate Lndata1 whose A input receive f'.
Output of this gate is sent to B input of Lndata2 gate whose A input receive f` and whose output go inside register.

• If f' is 0 then Lndata1 receive register value on A input and 0 on B iput so register value remains the same
  
• If f' is 1 then NOT(NOT(Data)) so Data arrive on register so data is loaded inside register
  

Register read

Operating principle

To read a register it is needed to generate a read command and to ge the data from register output
In wireworld computer data flows ou register on wire located at left of register bank and will fall along a stream of logic gates
Read command is generated at level of a signle register. She must be synchronised with register loop so that first bit of value contained in register be at register output at the same time than the first electron of read command
Read command is generated by register read access controler via 2 electron bursts

• One that raise along a wire located on the left of read logic
• One that fall along a wire located onthe left of previous wire

Cells located in output of each register should implement the following features:

• Propagation of read data to the bottom of register bank
• Propagation of rising and falling burst along register bank
• Read data of register selected by collision of falling and rising electron bursts

Implementation

Read logic is composed of following gates :

• 2 AND NOT gates called Lsel1 Lsel2
• A double AND NOT gate called X
• 1 transistor Tr

Read of register data is done thanks Lsel1 and Lsel2 logic gates which implement the following function:

• f = (rising_burst AND NOT ( rising_burst AND NOT falling_burst))

By this way f is 1 only where there is the collision of the 2 bursts.

X receive f on left input and data read from upper register on right input, its left output is bound on right input of below register gate X , its right output is bound to input of transistor Tr and income timings are computed so that:

• If f is 0 data read is propagated to bottom of register bank
  
• If f is 1 X right output is f'=f

f' is send to input of transistor Tr driven by value contained in register and its output is bound to right input of register below X gate
Transistor output is f' in case register data bit is 0, so we obtain NOT(register data) at transistor output

Special registers

They allow to perform other operations than simple read/write
Registers left/right SHIFT deal with leng of wire that ellectron follow to the register output to expose bit[1] or le bit[15] at the time bit[0] shoudl be exposed.
Registers NOT, AND NOT respectively use NOT, AND NOT gates to implement the feature

Adder register

It use a binary adder to compute sum of inputs
Remark : in case of overflow, RS flip-flop used to propagate carry will still be set when bit[0] of input registers will come back again inot adder inputs so result will be R60 + R61 + 1
This particularit is used in prime computation algorithm that work with 1 complement arithmetic. In this case -1 is coded 0xFFFE and 1 is coded 0x0001 which give 0xFFFF when we sum them so -0 in 1 complement arithmetic
To easily detect a null sum using conditional register program first execute and overflow operationlike by example 0xFFF6 + 0xFFFE ( -9 -1 ) which return 0xFFF5 (-10) with carry at 1 so when 10 is added the result is 0xA + 0xFFF5 + 1 = 0x0 which will be well detected by conditional register.

Conditional register

Read of Register R56 return R55 if R56 is not null else R57

Internal architecture

This feature is implemented using the following components:

• 2 RS Flip-Flops FF1 and FF2
• 3 transistors T1,T2,T3
• An OR gate
• A reset loop whose period is the same than register storage loop
• An electron generator in 6 microns

Operating

Reset loop put flip-flop FF1 to 0 and flip-flop FF2 to 1

• Case R56 not null

Value stored in R56 contains a bit ar 1 so FF1 is set to 1 which set FF2 to 0
As FF2 is at 0 T3 is unlocked so electrons emitted by generator lock T2 so R57 value don't reach OR gate
FF2 is at 1 so T1 is unlocked what let electrons stored in R55 reach OR gate

• Case R56 null

Value stored in R56 does not contain bit at 1 so FF1 is set at 0 and FF2 remains at 1
As FF2 is at 1 T3 is locked so electrons emitted by generator don`t reach T2, consequently T2 is unlocked so electrons stored in R57 reach OR gate
FF2 is at 1 so T1 is locked so electrons stored in R55 don't reach OR gate

Register configuration

To make easier the execution of other software than the one provided with wireworld computer I wrote a generic configuration file for the desing that allow to define the content of each register at simulation startup via a configuration file.
By automatising generation if configuration file, corresponding to a software written in assembly, by the functionnal model of wireworld computer it become easy to execute them on the design

Wireworld computer

Functional model

Wireworld computer design is complex and execution of a single instruction take several hundred of generations
To te able to easily test and develop small programs for wireworld computer I developed a functional model in C++ language which reproduce execution pipeline and register behaviours
It generates too the configuration file corresponding to program to execute which will load registers with values necessary to execute program on Wireworld computer design.

Inputs/Outputs

Model receive the following parameters:

• Name of file containing program to execute written in assembly
• optional parameter --detailled_display to activate or not operating details of binary/BCD converter
• optional parameter --instruction_delay to define tempo duration ( in ms ) between each instruction
• optional parameter --output_file to define the name of configuration and generate it

Usage is :
        wireworld.exe [OPTIONS] <program_file>
OPTIONS : --<parameter_name>=<parameter_value>
        --detailled_display=...
        --instruction_delay=...
        --output_file=...

During its execution functional model display the following information:

• Cycle number
• PC value
• Instruction value
• Instruction mnemonic
• Source register => Read value => Destination register
• Value displayed in case of write in R0 register.

Remark : functional model don't take in account delays needed to latch R0 value so in case of closer write functional model will indicate them as displayed whereas with real wireworld computer design first value would perhaps not had time to be be displayed before the second one be take in account.

***** Starting cycle 10*****
PC value :=> PC = 0xb
=> Instruction = 0x3b29
=> MOV R59, R41
R41 => 0x0 => R59
***** Starting cycle 11*****
PC value :=> PC = 0xc
=> Instruction = 0x30
=> MOV R0, R48
R48 => 0x0 => R0
-----------------------------------
** DISPLAY => 0
-----------------------------------
***** Starting cycle 12*****
PC value :=> PC = 0xd
=> Instruction = 0x3d3b
=> MOV R61, R59
R59 => 0x0 => R61

In case detailled_display has been activated the ouput will display details of internal operating of Binary/BCD converter

Assembly format

Assembly format used as input of functional simulator is very simple :

• Comments start with a ; and end with line return
• There is one line per register with the following syntax

register_number : [<optional_label> :] (Value | Instruction ) 

By example:

; Register | Action on read                           | Action on write
;----------------------------------------------------------------------------------------
; R0       | Returns zero                             | Writes value to display module
; R1-R52   | Reads value from register                | Writes value to register
; R53      | Returns bitwise AND of R54 with NOT R53  | Writes value to register
; R54      | Returns bitwise AND of R53 with NOT R54  | Writes value to register
; R55      | Returns zero                             | Writes value to register
; R56      | Returns value in R55 if register R56 is  | Writes value to register
;          | non-zero, and the value in R57 otherwise | 
; R57      | Returns zero                             | Writes value to register
; R58      | Returns R58 rotated right one place      | Writes value to register
; R59      | Returns R59 rotated left one place       | Writes value to register
; R60      | Reads value from register                | Writes value to register
; R61      | Returns sum of R60 and R61               | Writes value to register
; R62      | Reads NOT R62                            | Writes value to register
; R63      | Returns program counter value            | Causes branch to given target
;----------------------------------------------------------------------------------------
 0 :       UNUSED
 1 :       MOV R62, R42 ; Compute negative value of upper limit
 2 :       MOV R55, R47 ; Prepare branch if limit non reached
 3 :       MOV R57, R44 ; Prepare branch if limit reached
 4 :       MOV R61, R50 ; Load -1 in adder as second operand
 5 :       MOV R60, R62 ; negative (upper limit - 1) as first operand of adder
 6 :       MOV R60, R61 ; perform addition to set the Carry
 7 :       MOV R61, R41 ; current variable as second operand of adder
 8 :       MOV R56, R61 ; perform addition
 9 :       MOV R63, R56 ; Branch on addition result
10 :       MOV R59, R41 ; Prepare computation of 2 * V
11 :       MOV R0 , R48 ; Display square of variable
12 :       MOV R61, R59 ; Prepare computation of 2 * V + square(V) by setting 2 * V as second operand of adder
13 :       MOV R60, R48 ; Prepare computation of 2 * V + square(V) by setting square(V) as first operand of adder
14 :       MOV R61, R61 ; Compute addition of 2 * V + square(V) and set it as second operand of adder
15 :       MOV R60, R45 ; Preparing addition of increment by setting 1 as first operad of adder
16 :       MOV R48, R61 ; Compute the new square value and store it
17 :       MOV R61, R41 ; Prepare V + 1 by setting V as second operand of adder
18 :       MOV R63, R43 ; Preparing branch at the beginning of the loop
19 :       MOV R41, R61 ; Incrementing current variable
20 :       MOV R63, R44 ; Branching on end of the loop
21 :       MOV R0 , R46 ; End of loop
22 :       0x0000
23 :       0x0000
24 :       0x0000
25 :       0x0000
26 :       0x0000
27 :       0x0000
28 :       0x0000
29 :       0x0000
30 :       0x0000
31 :       0x0000
32 :       0x0000
33 :       0x0000
34 :       0x0000
35 :       0x0000
36 :       0x0000
37 :       0x0000
38 :       0x0000
39 :       0x0000
40 :       0x0000
41 : <V> : 0x0000       ; Initialisation running variable to 0
42 :       0x000a       ; Set upper limit - 1
43 :       0x0004       ; Branch value to restart the loop
44 :       0x0014       ; Branch value to end the loop
45 :       0x0001       ; Increment value
46 :       0xffff       ; Final value
47 :       0x000a       ; Branch value to continue the loop
48 : <SQ>: 0x0000       ; Current square value
49 : <DB>: 0x0000       ; Store double of current value
50 :       0xfffe       ;  -1
51 :       0x0000
52 :       0x0000
53 :       UNUSED
54 :       UNUSED
55 :       UNUSED
56 :       UNUSED
57 :       UNUSED
58 :       UNUSED
59 :       UNUSED
60 :       0x0000
61 :       UNUSED
62 :       UNUSED
63 : <PC>: 0x0001       ; Initial PC

Use

Functional model allowed me to test development of programs for wireworld computer.
By example a loop to display square of first ten integers. Interest of this program is to succeed to compute successive square despite the lack of multiplication.
It is based on the fact that pow(n+1,2) = pow(n,2) + 2 * n + 1 which is 2 additions and one shift in case previous square value has been stored.
I wanted to use this principle to optimise the prime number computation program provided with wireworld computer assuming it is not necessary to search divisor greater than square_root(n) to determine if n is prime
As computing square_root(n) is not so easy I decided to start from minimum square and root: 1 and 1 and then to compute next square and root at each time new candidate is greater than current square.
The goal was to limit the number of time substraction loop is executed to simulate division of prime candidate p by divisor q
It is equivalent to divide the number of divisions of candidate p by 2 but increase code complexity:

• It is needed to perform a more complex test on p and q : comparison with square_root and square which imply substrction and result sign check
• It requires more test instruction with branch preparation it implies

Given the URISC architecture of wireworld computer if leads to an important code expansion which finally cancel the gain coming from reduce number of division and make alogrithm slightly slower than original one by using near the whole registers of processor.
The last point forced me to carrefully think the way to write the code and to correctly use register init values to succeed to make the wole program take place in registers

Conclusions

I'm still fascinated by this cellular automaton that allow to simulate such complex thinks like a small URISC processor with 64 registers of 16 bits depite its simple rules.
Wireworld Computer allowed me to discover architectures URISC and TTA I was not aware of before and that I plan to reuse in my FPGA experimentations
The time spend to develop for Wireworld Computer make me also conscious of the limitations of this kind of architecture.
Reverse engineering of Wireworld Computer design increased my admiration for those who designed it and I still find a kind of magic when seeing it in simulation despite I now understand its details