# Divisible-by-2 Circuit Help!

I'm having a little trouble with my boolean algebra and I was hoping you all can help me out. I've been given the task of designing a circuit that takes in a binary 4 digit number (X3X2X1X0) and returns '1' if the number entered was even. I'm fairly certain that my truth table is correct, but if someone could look at my algebra for my 'Y' value, it would be greatly appreciated, as I am somewhat unfamiliar with boolean algebra. Thanks in advance!

• Your algebra is definitely wrong, because it didn't reduce to the final trivial equation. – Ignacio Vazquez-Abrams Oct 14 '14 at 21:12
• And now that I take a close look at it, terms 4 and 8 in the first step are wrong. – Ignacio Vazquez-Abrams Oct 14 '14 at 21:13

i.e. $Y = \bar{X_0}$
It's clearly this because if $X_0$ is 1 then the number is an odd number. Sometimes you've just got to look at the truth table without thinking much about boolean algebra.