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! enter image description here

  • \$\begingroup\$ Your algebra is definitely wrong, because it didn't reduce to the final trivial equation. \$\endgroup\$ Commented Oct 14, 2014 at 21:12
  • \$\begingroup\$ And now that I take a close look at it, terms 4 and 8 in the first step are wrong. \$\endgroup\$ Commented Oct 14, 2014 at 21:13

1 Answer 1


The answer is the inverse of X0

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.

  • \$\begingroup\$ Wow I feel dumb for looking past that. Thanks for the help! \$\endgroup\$
    – MattKos
    Commented Oct 14, 2014 at 21:36
  • \$\begingroup\$ Most of my best "AHA" moments comes from squinting my eyes while looking at truth tables. \$\endgroup\$
    – slebetman
    Commented Oct 15, 2014 at 4:18

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