# Homework Help: Simplifying a boolean equation

1. Jan 28, 2010

### triden

1. The problem statement, all variables and given/known data

$$X = A\overline{D}+\overline{B}AC+\overline{B}\overline{D}\overline{C}+BA\overline{C}$$

2. Relevant equations

I need to try to simplify or reduce that boolean equation to something as small as possible.

3. The attempt at a solution

It used to be worse and I used a karnaugh map to get to where I am now from a truth table. I am having trouble getting anything better. I can reduce it to get an XOR gate, but I think it can do better. Any tips?

Thanks

Last edited: Jan 29, 2010
2. Jan 28, 2010

### story645

Last edited: Jan 28, 2010
3. Jan 29, 2010

### snarfherder

You can reduce gate inputs by collecting terms, but this is as simplified as it gets. Draw the k-map. A(B xor C + D') + B'C'D'

Last edited: Jan 29, 2010