Question

I have 2 programs: X and Y.

X has two bitmaps A and C.

X calls Y.

Y has a bitMap B.

The code I need to execute in Y is

if AB == B && BC == C 
    //do some action Z

I want to combine on A and C using boolean operations such that I can pass a single bitMap to Y. This single bitmap can then do any boolean operation with B to return true / false and accordingly I can decide to do action Z.

Answer 1

There is no way to simplify by combining A and C.

Here is our truth table:

B A C  Z
0 0 0  1
0 0 1  0
0 1 0  1
0 1 1  0
1 0 0  0
1 0 1  0
1 1 0  1
1 1 1  1

We can see from the truth table that when B = 0, we have Z = not C; when B = 1, we have Z = A.

Suppose for the sake of contradiction that we have a one-bit function Y = f(A, C) that “summarizes” A and C. We use B to choose whether the summary equals ‘not C’ versus ‘A’. But this is clearly impossible, because a single bit cannot preserve enough information to be able to extract the value ‘not C’ and also the value ‘A’.