Need help with Carry In Truth Tables!!!?

Question

I am working with the below "Carry in" Truth Table

A B C SUM
0 0 0 0
0 0 1 1
0 1 0 1
0 1 1 0
1 0 0 1
1 0 1 0
1 1 0 0
1 1 1 1

and have to convert it into an expression using AND, NOT, OR

I have come up with this:

(A & B & C)+(A & -B & -C)+(-A & B -C)+(-A & -B & C)

It uses a combination of 16 AND, NOT, OR.

How do I get this down to using only 8? Thanks

How do I show XOR C?

Answer 1

The minimum solution is (A XOR B) XOR C and you make an XOR as (A & -B) + (-A & B ) and requires 2 NOT's, 2 AND's, and a single OR. Using only 2 input logic functions, I'm not sure it can be done with less than that.


Doug