the table of logic and ($\wedge$) is

0 0 0
0 1 0
1 0 0
1 1 1

I can build a "logic and" operation with additions and subtractions?

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I don't think so, but you can do it with addition, subtraction, and logical or. – Dan Brumleve Jan 11 '12 at 3:52

If you mean truncated subtraction, so that negative results are truncated to zero, that is, $x\dot-y=0$ when $x\leq y$, then since $\neg x=1\dot-x$, it follows that de Morgan's law amounts to $$x\wedge y=1\dot-\Bigl((1\dot-x)+(1\dot- y)\Bigr),$$ which is what you want.
this is the same of $(x+y)\dot- 1$ ? – juanpablo Jan 11 '12 at 21:21