If I have a truth table, is there a way of determining the bitwise expression I need for that truth table?

Question

I am attempting to do the following in c:

unsigned int mask;
unsigned int previous;
unsigned int new;
unsigned int out;

for( int i = 0; i < 8; ++i )
{
    bool bit_set = GET_BIT( mask, i );

    // If the mask bit is true, use the new bit, otherwise use the previous bit
    SET_BIT( out, i, GET_BIT( bit_set ? new : previous, i ) );
}

However I think there may be an easier and quicker way using bitwise operations. I have the truth table but I don't know how to get the expression I need.

Truth table is:

m | p | n | o
0 | 0 | 0 | 0
1 | 0 | 0 | 0
0 | 1 | 0 | 1
1 | 1 | 0 | 0
0 | 0 | 1 | 0
1 | 0 | 1 | 1
0 | 1 | 1 | 1
1 | 1 | 1 | 1

How would I go about working this out?

Answer 1

Use Karnaugh Map - there is a solver available online. Pick "three values", enter the expected results for all eight combinations, and use the expression the solver produces:

F(m, p, n) = (p & !n) | (m & n)

EDIT : You can expand this solution to do the whole byte at once, rather than doing it one bit at a time, by using the ~ bitwise NOT operator:

result = (mask & new) | (~mask & previous);

Answer 2

If the mask bit is true, use the new bit, otherwise use the previous bit

The natural way to express this (to me) is (mask & new) | (~mask & previous). That is to say, mask corresponding bits from new and previous, and add them together using OR.