bilbo

April 18th, 2005, 04:53

Hi all,

how can we prove that:

can be replaced by

???

Well, the "bruteforce" demonstration is obvious: we test the whole space for inputs (with SPACE 1 as well as 256 for X,Y,Z: it is enough the case one-bit)

but, is there some more elegant demonstration?

Thanks, bilbo

how can we prove that:

Code:

(X and Y) or (notX and Z)

Code:

(Z xor (X and (Y xor Z)))

Well, the "bruteforce" demonstration is obvious: we test the whole space for inputs (with SPACE 1 as well as 256 for X,Y,Z: it is enough the case one-bit)

Code:

#include <stdio.h>

#define SPACE 1

void

main(void)

{

int X, Y, Z;

for (X=0; X<SPACE; X++) for (Y=0; Y<SPACE; Y++) for (Z=0; Z<SPACE; Z++)

if ((X&Y | (~X&SPACE-1)&Z) != (Z ^ (X & (Y^Z)))) {

printf("ko: X=%d, Y=%d, Z=%d\n", X, Y, Z);

return;

}

printf("ok\n";

}

but, is there some more elegant demonstration?

Thanks, bilbo