NAND gates
NOT
!A
!(A & A)
AND
A & B
!!(A & B)
OR
A | B
!!(A | B)
!(!A & !B)
XOR, 6 gates
(A | B) & !(A & B)
XOR, 5 gates
(A & !B) | (!A & B)
!!((A & !B) | (!A & B))
!(!(A & !B) & !(!A & B))
XOR, 4 gates
(A & !B) | (!A & B)
(A & !A) | (A & !B) | (B & !A) | (B & !B)
A & (!A | !B) | B & (!A | !B)
A & !(A & B) | B & !(A & B)
!(!(A & !(A & B)) & !(B & !(A & B)))
NOR
XNOR
