Name
Silicon::Chip - Design a silicon chip by combining logic gates and sub chips.
Synopsis
Create and simulate the operation of a 4-bit comparator. Given two 4-bit unsigned integers, the comparator indicates whether the first integer is greater than the second:
my $B = 4;
my $c = Silicon::Chip::newChip(title=>"$B Bit Compare");
$c->input( "a$_") for 1..$B; # First number
$c->input( "b$_") for 1..$B; # Second number
$c->gate("nxor", "e$_", {1=>"a$_", 2=>"b$_"}) for 1..$B-1; # Test each bit for equality
$c->gate("gt", "g$_", {1=>"a$_", 2=>"b$_"}) for 1..$B; # Test each bit pair for greater
for my $b(2..$B)
{$c->and( "c$b", {(map {$_=>"e$_"} 1..$b-1), $b=>"g$b"}); # Greater on one bit and all preceding bits are equal
}
$c->gate("or", "or", {1=>"g1", (map {$_=>"c$_"} 2..$B)}); # Any set bit indicates that 'a' is greater than 'b'
$c->output( "out", "or"); # Output 1 if a > b else 0
my $t = $c->simulate({a1=>1, a2=>1, a3=>1, a4=>0,
b1=>1, b2=>0, b3=>1, b4=>0},
svg=>"svg/Compare$B"); # Svg drawing of layout
is_deeply($t->values->{out}, 1);To obtain:
Other circuit diagrams can be seen in folder: lib/Silicon/svg
Description
Design a silicon chip by combining logic gates and sub chips.
Version 20231028.
The following sections describe the methods in each functional area of this module. For an alphabetic listing of all methods by name see Index.
Construct
Construct a Silicon chip using standard logic gates.
newChip(%options)
Create a new chip.
Parameter Description
1 %options OptionsExample:
if (1) # Single AND gate
{my $c = Silicon::Chip::newChip; # 𝗘𝘅𝗮𝗺𝗽𝗹𝗲
$c->input ("i1");
$c->input ("i2");
$c->and ("and1", {1=>q(i1), 2=>q(i2)});
$c->output("o", "and1");
my $s = $c->simulate({i1=>1, i2=>1});
ok($s->steps == 2);
ok($s->values->{and1} == 1);
}gate($chip, $type, $output, $inputs)
A logic gate of some sort to be added to the chip.
Parameter Description
1 $chip Chip
2 $type Gate type
3 $output Output name
4 $inputs Input names to output from another gateExample:
if (1) # Two AND gates driving an OR gate a tree # 𝗘𝘅𝗮𝗺𝗽𝗹𝗲
{my $c = newChip;
$c->input ("i11");
$c->input ("i12");
$c->and ("and1", {1=>q(i11), 2=>q(i12)});
$c->input ("i21");
$c->input ("i22");
$c->and ("and2", {1=>q(i21), 2=>q(i22)});
$c->or ("or", {1=>q(and1), 2=>q(and2)});
$c->output( "o", "or");
my $s = $c->simulate({i11=>1, i12=>1, i21=>1, i22=>1});
ok($s->steps == 3);
ok($s->values->{or} == 1);
$s = $c->simulate({i11=>1, i12=>0, i21=>1, i22=>1});
ok($s->steps == 3);
ok($s->values->{or} == 1);
$s = $c->simulate({i11=>1, i12=>0, i21=>1, i22=>0});
ok($s->steps == 3);
ok($s->values->{o} == 0);
}install($chip, $subChip, $inputs, $outputs, %options)
Install a chip within another chip specifying the connections between the inner and outer chip. The same chip can be installed multiple times as each chip description is read only.
Parameter Description
1 $chip Outer chip
2 $subChip Inner chip
3 $inputs Inputs of inner chip to to outputs of outer chip
4 $outputs Outputs of inner chip to inputs of outer chip
5 %options OptionsExample:
if (1) # Install one inside another chip, specifically one chip that performs NOT is installed three times sequentially to flip a value
{my $i = newChip(name=>"inner");
$i->input ("Ii");
$i->not ("In", "Ii");
$i->output("Io", "In");
my $o = newChip(name=>"outer");
$o->input ("Oi1");
$o->output("Oo1", "Oi1");
$o->input ("Oi2");
$o->output("Oo", "Oi2");
$o->install($i, {Ii=>"Oo1"}, {Io=>"Oi2"}); # 𝗘𝘅𝗮𝗺𝗽𝗹𝗲
my $s = $o->simulate({Oi1=>1}, dumpGatesOff=>"dump/not1", svg=>"svg/not1");
is_deeply($s, {steps => 2,
changed => { "(inner 1 In)" => 0, "Oo" => 1 },
values => { "(inner 1 In)" => 0, "Oi1" => 1, "Oo" => 0 },
svg => "svg/not1.svg"});
}Basic Circuits
Some well known basic circuits.
compareEq($bits, %options)
Compare two unsigned binary integers a, b of a specified width. Output 1 if a is equal to b else 0.
Parameter Description
1 $bits Bits
2 %options OptionsExample:
if (1) # Compare 8 bit unsigned integers 'a' == 'b' - the pins used to input 'a' must be alphabetically less than those used for 'b'
{my $B = 4;
my $c = Silicon::Chip::compareEq($B); # 𝗘𝘅𝗮𝗺𝗽𝗹𝗲
my %a = map {("a0$_"=>0)} 1..$B;
my %b = map {("b0$_"=>0)} 1..$B;
my $s = $c->simulate({%a, %b, "a02"=>1, "b02"=>1}, svg=>"svg/CompareEq$B"); # Svg drawing of layout
# my $s = $c->simulate({%a, %b, "a02"=>1, "b02"=>1}); # Equal: a == b
is_deeply($s->values->{out}, 1); # Equal
is_deeply($s->steps, 3); # Which goes to show that the comparator operates in O(4) time
my $t = $c->simulate({%a, %b, "b02"=>1}); # Less: a < b
is_deeply($t->values->{out}, 0); # Not equal
is_deeply($t->steps, 3); # Which goes to show that the comparator operates in O(4) time
}compareGt($bits, %options)
Compare two unsigned binary integers a, b of a specified width. Output 1 if a is greater than b else 0.
Parameter Description
1 $bits Bits
2 %options OptionsExample:
if (1) # Compare 8 bit unsigned integers 'a' > 'b' - the pins used to input 'a' must be alphabetically less than those used for 'b'
{my $B = 8;
my $c = Silicon::Chip::compareGt($B); # 𝗘𝘅𝗮𝗺𝗽𝗹𝗲
my %a = map {("a00$_"=>0)} 1..$B;
my %b = map {("b00$_"=>0)} 1..$B;
# my $s = $c->simulate({%a, %b, "a002"=>1}, svg=>"svg/CompareGt$B"); # Svg drawing of layout
my $s = $c->simulate({%a, %b, "a002"=>1}); # Greater: a > b
is_deeply($s->values->{out}, 1);
is_deeply($s->steps, 4); # Which goes to show that the comparator operates in O(4) time
my $t = $c->simulate({%a, %b, "b002"=>1}); # Less: a < b
is_deeply($t->values->{out}, 0);
is_deeply($t->steps, 4); # Which goes to show that the comparator operates in O(4) time
}compareLt($bits, %options)
Compare two unsigned binary integers a, b of a specified width. Output 1 if a is less than b else 0.
Parameter Description
1 $bits Bits
2 %options OptionsExample:
if (1) # Compare 8 bit unsigned integers 'a' < 'b' - the pins used to input 'a' must be alphabetically less than those used for 'b'
{my $B = 8;
my $c = Silicon::Chip::compareLt($B); # 𝗘𝘅𝗮𝗺𝗽𝗹𝗲
my %a = map {("a00$_"=>0)} 1..$B;
my %b = map {("b00$_"=>0)} 1..$B;
# my $s = $c->simulate({%a, %b, "a002"=>1}, svg=>"svg/CompareLt$B"); # Svg drawing of layout
my $s = $c->simulate({%a, %b, "b002"=>1}); # Less: a < b
is_deeply($s->values->{out}, 1);
is_deeply($s->steps, 4); # Which goes to show that the comparator operates in O(4) time
my $t = $c->simulate({%a, %b, "a002"=>1}); # Greater: a > b
is_deeply($t->values->{out}, 0);
is_deeply($t->steps, 4); # Which goes to show that the comparator operates in O(4) time
}pointToInteger($bits, %options)
Convert a mask known to have at most a single bit on - also known as a point mask - to an output number representing the location in the mask of the bit set to 1. If no such bit exists in the point mask then output is 0.
Parameter Description
1 $bits Bits
2 %options OptionsExample:
if (1)
{my $B = 4;
my $c = pointToInteger($B); # 𝗘𝘅𝗮𝗺𝗽𝗹𝗲
my %i = map {(sprintf("i%02d", $_)=>0)} 1..2**$B-1;
$i{i05} = 1;
my $s = $c->simulate(\%i, svg=>"svg/point$B");
is_deeply($s->steps, 2);
is_deeply($s->values->{o01}, 1);
is_deeply($s->values->{o02}, 0);
is_deeply($s->values->{o03}, 1);
is_deeply($s->values->{o04}, 0);
}monotoneMaskToInteger($bits, %options)
Convert a monotone mask to an output number representing the location in the mask of the bit set to 1. If no such bit exists in the point then output is 0.
Parameter Description
1 $bits Bits
2 %options OptionsExample:
if (1)
{my $B = 4;
my $c = monotoneMaskToInteger($B); # 𝗘𝘅𝗮𝗺𝗽𝗹𝗲
my %i = map {(sprintf("i%02d", $_)=>1)} 1..2**$B-1;
$i{"i0$_"} = 0 for 1..6;
my $s = $c->simulate(\%i, svg=>"svg/monotoneMask$B");
is_deeply($s->steps, 4);
is_deeply($s->values->{o01}, 1);
is_deeply($s->values->{o02}, 1);
is_deeply($s->values->{o03}, 1);
is_deeply($s->values->{o04}, 0);
}chooseWordUnderMask($words, $bits, %options)
Choose one of a specified number of words, each of a specified width, using a point mask.
Parameter Description
1 $words Number of words
2 $bits Bits in each word
3 %options OptionsExample:
if (1)
{my $B = 2; my $W = 2;
my $c = chooseWordUnderMask($W, $B); # 𝗘𝘅𝗮𝗺𝗽𝗹𝗲
my %i;
for my $w(1..$W)
{my $s = sprintf "%0${B}b", $w;
for my $b(1..$B)
{my $c = sprintf "w%1d_%1d", $w, $b;
$i{$c} = substr($s, -$b, 1);
}
}
my %m = map{("m$_"=>0)} 1..$W;
my $s = $c->simulate({%i, %m, "m1"=>1}, svg=>"svg/choose_${W}_$B");
is_deeply($s->steps, 3);
is_deeply($s->values->{o1}, 1);
is_deeply($s->values->{o2}, 0);
}findWord($words, $bits, %options)
Choose one of a specified number of words, each of a specified width, using a key. Return a mask indicating the locations of the key or an empty mask if the key is not present.
Parameter Description
1 $words Number of words
2 $bits Bits in each word and key
3 %options OptionsExample:
if (1)
{my $B = 2; my $W = 2;
my $c = findWord($W, $B); # 𝗘𝘅𝗮𝗺𝗽𝗹𝗲
my %i;
for my $w(1..$W)
{my $s = sprintf "%0${B}b", $w;
for my $b(1..$B)
{my $c = sprintf "w%1d_%1d", $w, $b;
$i{$c} = substr($s, -$b, 1);
}
}
my %m = map{("m$_"=>0)} 1..$W;
if (1) # Find key 2 at position 2
{my $s = $c->simulate({%i, %m, "k2"=>1, "k1"=>0}, svg=>"svg/findWord_${W}_$B");
is_deeply($s->steps, 3);
is_deeply($s->values->{o1}, 0);
is_deeply($s->values->{o2}, 1);
}
if (1) # Find key 1 at position 1
{my $s = $c->simulate({%i, %m, "k2"=>0, "k1"=>1});
is_deeply($s->steps, 3);
is_deeply($s->values->{o1}, 1);
is_deeply($s->values->{o2}, 0);
}
if (1) # Find key 0 - does not exist
{my $s = $c->simulate({%i, %m, "k2"=>0, "k1"=>0});
is_deeply($s->steps, 3);
is_deeply($s->values->{o1}, 0);
is_deeply($s->values->{o2}, 0);
}
if (1) # Find key 3 - does not exist
{my $s = $c->simulate({%i, %m, "k2"=>1, "k1"=>1});
is_deeply($s->steps, 3);
is_deeply($s->values->{o1}, 0);
is_deeply($s->values->{o2}, 0);
}
}Simulate
Simulate the behavior of the chip.
simulate($chip, $inputs, %options)
Simulate the action of the logic gates on a chip for a given set of inputs until the output values of each logic gate stabilize.
Parameter Description
1 $chip Chip
2 $inputs Hash of input names to values
3 %options OptionsExample:
if (1)
{my $i = newChip(name=>"inner");
$i->input ("Ii");
$i->not ("In", "Ii");
$i->output( "Io", "In");
my $o = newChip(name=>"outer");
$o->input ("Oi1");
$o->output("Oo1", "Oi1");
$o->input ("Oi2");
$o->output("Oo2", "Oi2");
$o->input ("Oi3");
$o->output("Oo3", "Oi3");
$o->input ("Oi4");
$o->output("Oo", "Oi4");
$o->install($i, {Ii=>"Oo1"}, {Io=>"Oi2"});
$o->install($i, {Ii=>"Oo2"}, {Io=>"Oi3"});
$o->install($i, {Ii=>"Oo3"}, {Io=>"Oi4"});
my $s = $o->simulate({Oi1=>1}, dumpGatesOff=>"dump/not3", svg=>"svg/not3"); # 𝗘𝘅𝗮𝗺𝗽𝗹𝗲
is_deeply($s->values->{Oo}, 0);
is_deeply($s->steps, 4);
}Hash Definitions
Silicon::Chip Definition
Chip description
Output fields
gates
Gates in chip
installs
Chips installed within the chip
name
Name of chip
title
Title if known
Private Methods
AUTOLOAD($chip, @options)
Autoload by logic gate name to provide a more readable way to specify the logic gates on a chip.
Parameter Description
1 $chip Chip
2 @options OptionsIndex
1 AUTOLOAD - Autoload by logic gate name to provide a more readable way to specify the logic gates on a chip.
2 chooseWordUnderMask - Choose one of a specified number of words, each of a specified width, using a point mask.
3 compareEq - Compare two unsigned binary integers a, b of a specified width.
4 compareGt - Compare two unsigned binary integers a, b of a specified width.
5 compareLt - Compare two unsigned binary integers a, b of a specified width.
6 findWord - Choose one of a specified number of words, each of a specified width, using a key.
7 gate - A logic gate of some sort to be added to the chip.
8 install - Install a chip within another chip specifying the connections between the inner and outer chip.
9 monotoneMaskToInteger - Convert a monotone mask to an output number representing the location in the mask of the bit set to 1.
10 newChip - Create a new chip.
11 pointToInteger - Convert a mask known to have at most a single bit on - also known as a point mask - to an output number representing the location in the mask of the bit set to 1.
12 simulate - Simulate the action of the logic gates on a chip for a given set of inputs until the output values of each logic gate stabilize.
Installation
This module is written in 100% Pure Perl and, thus, it is easy to read, comprehend, use, modify and install via cpan:
sudo cpan install Silicon::ChipAuthor
Copyright
Copyright (c) 2016-2023 Philip R Brenan.
This module is free software. It may be used, redistributed and/or modified under the same terms as Perl itself.