XOR using NAND gates
We know that xor means
(x' ^ y) v (x ^ y')
So I tried rearranging this equations. Distributing a little, I got.
(x v y) ^ (y' v y) ^ (x' v x) ^ (y' v x')
(y' v y) is always true, as is ('x v x)
So we get
(x v y ) ^ (y' v x')
or, by De Morgans laws
(x' ^ y')' ^ (y ^ x)'
But we must use all nands! We can use this boolean equation
(z' ^ 1)' = z
to get
(((x' ^ y')' ^ (y ^ x)')' ^ 1)'
Ben Brinckerhoff
Monday, October 13, 2003
That does solve the problem, but not optimally. Only 4 NAND gates are required. This is a problem from the days of old when NAND gates came 4 to a DIP.
Andrew P. Lentvorski, Jr.
Thursday, December 4, 2003
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