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I've tried every which way I can think of to manipulate the algebra using the various laws I was given, but I cannot figure out a way to get $\overline{x+y}$ to convert to only NAND operations using $\overline{x\cdot x}$, $\overline{x\cdot y}$, or $\overline{y\cdot y}$

I've tried using idempotent, DeMorgan's, identity, and double negation laws to no avail.

Mirrana
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1 Answers1

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I’ll use $\mid$ for the connective NAND. You want $\overline{x+y}$; as a first step, this is $(x+y)\mid(x+y)$. Now check that $x+y=(x\mid x)\mid(y\mid y)$, and put the pieces together.

Brian M. Scott
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  • sigh I've spent a good hour doing various things and I did get to that as a first step, but I can't believe I didn't see that I could easily convert the two $x+y$ to $\overline{\overline{x\cdot x}\cdot\overline{y\cdot y}}$ – Mirrana Feb 07 '13 at 04:07
  • @agent154: Trust me, I know the feeling! – Brian M. Scott Feb 07 '13 at 04:09