shrinquem's Introduction

shrinquem

An algorithm for Boolean logic minimization. Shrinquem finds a minimum sum-of-products representation for a given a truth table.

1. An Example

Consider the following truth table with three Boolean inputs:

n	A	B	C	f(A, B, C)
0	0	0	0	1
1	0	0	1	1
2	0	1	0	0
3	0	1	1	1
4	1	0	0	1
5	1	0	1	0
6	1	1	0	0
7	1	1	1	0

Shrinquem can be used to find a minimum sum-of-products representation for this Boolean function as follows:

#include <stdlib.h>
#include <stdio.h>
#include "shrinquem.h"

int main(int argc, char* argv[])
{
    const numVars = 3;
    const triLogic truthTable[8] = { 1,1,0,1,1,0,0,0 };
    SumOfProducts sumOfProducts = { numVars };
    ReduceLogic(truthTable, &sumOfProducts);
    GenerateEquationString(&sumOfProducts, NULL);
    printf("f(A, B, C) = %s", sumOfProducts.equation);
    FinalizeSumOfProducts(&sumOfProducts);

    return 0;
}

This code prints the following to standard out.

f(A, B, C) = A'C + B'C'

2. An Example with a "Don't Care"

Consider the following truth table with two Boolean inputs, where X indicates that we don't care what a particular output is:

n	A	B	f(A, B)
0	0	0	0
1	0	1	1
2	1	0	0
3	1	1	X

Shrinquem can be used to generate the equation as follows:

#include <stdlib.h>
#include <stdio.h>
#include "shrinquem.h"

int main(int argc, char* argv[])
{
    const numVars = 2;
    const triLogic truthTable[4] =
    {
        LOGIC_FALSE,
        LOGIC_TRUE,
        LOGIC_FALSE,
        LOGIC_DONT_CARE
    };
    SumOfProducts sumOfProducts = { numVars };
    ReduceLogic(truthTable, &sumOfProducts);
    GenerateEquationString(&sumOfProducts, NULL);
    printf("f(A, B) = %s", sumOfProducts.equation);
    FinalizeSumOfProducts(&sumOfProducts);

    return 0;
}