NAND Logic Equivalents

P||Q = !P|!Q = (P|P)|(Q|Q)
P&&Q = !(P|Q) = (P|Q)|(P|Q)
P|!Q = P|(P|Q) = P|(Q|Q) = !P || Q

P xor Q = (P|(P|Q))|(Q|(P|Q))
– (P && !Q) || (!P && Q))
– !(P|!Q) || !(!P|Q)
– (P|!Q)|(!P|Q)
= (P|(P|Q))|(Q|(P|Q))

S mux PQ = (!S|P)|(S|Q)
– (!S && P) || (S && Q)
– !(!S|P) || !(S|Q)
= (!S|P)|(S|Q)

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