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;

enter image description here


  • \$\begingroup\$ Can you write a truth table for the whole expression? \$\endgroup\$
    – The Photon
    Commented Oct 8, 2016 at 1:43
  • 4
    \$\begingroup\$ 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 \$\endgroup\$
    – jonk
    Commented Oct 8, 2016 at 2:08
  • \$\begingroup\$ @jonk - I erased the comment where I said you did a mistake because you didn't \$\endgroup\$ Commented Oct 8, 2016 at 7:02

1 Answer 1


This is the truth table: enter image description here

As you can see, it shows you how will the output react to different combinations of inputs. The "BOOLEAN" section shows the conditions for which that particular combination yields an output of 1 or TRUE. In other words, that is the algebraic expression for a TRUE output.

Now if any of these BOOLEAN expressions is 1, the output is also 1, so when you write f, you will put a + which signifies OR between them and obtain the rule for the circuit's behaviour.

Next you will simplify the equation. Take a look at this page. Find the appropriate rule and then use it to get your result. Don't worry, it should be headache free.

  • \$\begingroup\$ Thank you voters, I appreciate that you considered sending feedback to me \$\endgroup\$ Commented Apr 18, 2017 at 13:55

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