# Finding a cheaper implementation for XNOR logic gate

I'm looking for ways to simplify a configuration in which the output of an AND gate flows into an XNOR gate along with a third variable.

The function of such a configuration is as follows;

f(a,b,c) = (a*b) XNOR c


Using boolean algebra, how would you write that expression out so that it could be easily simplified?

A schematic is pasted in below;

Cheers

• Can you write a truth table for the whole expression? – The Photon Oct 8 '16 at 1:43
• Define cheaper. Define simpler. What's the price of an AND gate, a NOT gate, a 2-in MUX, and an XNOR? And does your logic include Q and Q' outputs? The expression is pretty easy, though: F = A' C' + B' C' + A B C = (A B)' C' + A B C – jonk Oct 8 '16 at 2:08
• @jonk - I erased the comment where I said you did a mistake because you didn't – Claudio Avi Chami Oct 8 '16 at 7:02