Maple Programs for Logic Design

Converting truth tables to simlified formulas

This program gives the simplified expression of a function given by a truth table.

> TF:=proc(binnum,charlist) local d,f,i,j,k,m,n; with(logic); n:=nops(charlist); for i to 2^n do m[i]:=true; for j to n do m[i]:=m[i] &and `if`(convert(2^n+i-1,base,2)[j]=1,charlist[n-j+1],&not(charlist[n-j+1])) od od; d:=convert(2^(2^n)+convert(binnum,decimal,binary),base,2); f:=false;for k to 2^n do f:=f &or `if`(d[k]=1,m[k],false) od; f:=bsimp(f) end:

Here are a few examples using it. Let be a function given by a truth table

> TF(0010,[p,q]);

Notice that we enter the values of from the truth table starting from the row of ones and ending on the row of zeroes. The variables and are entered inside square brackets, as a list. The next example explores function given by a truth table ordered from the row of zeroes to the row of ones. In that case we have to write the values of from the bottom to the top. Variables , , and are entered as a list, inside square brackets. The initial zero(es) in the binary representation of can be safely ignored.

> TF(1000111,[a,b,c]);

Now an example of a truth table with "doesn't matter" values ( on p. 213).

> tf:=n->TF(101000101+sum(convert(n+63,base,2)[t]*10^(t+9),t=1..6),[A,B,C,D]):

> gates:=seq(nops(tf(n)),n=1..64): min(gates);

> for n to 64 do if (gates[n]=2) then print(n) fi od;

> tf(1);

> tf(2);

> tf(18);

The last one is the simpliest.