# Boolean Simplification

I've been trying to simplify this equation:

Y = (¬AB + ¬C)(¬A + ¬D)


.. into this equation.

Y  = ¬A¬C + ¬C¬D + ¬AB


Unfortunately I keep going in circles with expanding and minimizing the booleans. Any tips or advice? Thanks.

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wolframalpha.com/input/… won't show you the steps it took to get all its answers, but may come in handy at some point... – MatrixFrog Oct 14 '10 at 9:54

## 1 Answer

Use the following simplification:

$\neg AB(\neg A + \neg D) = \neg AB\neg A + \neg AB\neg D = \neg AB + \neg AB\neg D = \neg AB$.

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Wow I realize I made a terrible mistake. I was cancelling ¬A¬AB because for some reason I thought ¬A¬A = 0 when in fact ¬A¬A = ¬A. Ugh.... thanks for the help! – Sam Oct 14 '10 at 3:42