All logic gates can be created using NAND logic gates.

Creating logic gates from NAND gates is called NAND logic.

NOT Gates

Y = A NAND A

NOT From NAND Truth Table

AY (A NAND A)
01
10

AND Gates

AND gates from NAND gates are basically negated NAND gates.

Y = P0 NAND P0 = (A NAND B) NAND (A NAND B)

AND From NAND Truth Table

ABP0 (A NAND B)Y (P0 NAND P0)
0010
0110
1010
1101

OR Gates

Y = P0 NAND P1 = (A NAND A) NAND (B NAND B)

OR From NAND Truth Table

ABP0 (A NAND A)P1 (B NAND B)Y (P0 NAND P1)
00110
01101
10011
11001

NOR Gates

NOR gates from NAND gates are basically negated OR gates.

Y = P2 NAND P2 = (P0 NAND P0) NAND (P1 NAND P1) = ((A NAND A) NAND (A NAND A)) NAND ((B NAND B) NAND (B NAND B))

NOR From NAND Truth Table

AB P0 (A NAND A)P1 (B NAND B)P2 (P0 NAND P1)P2 (P2 NAND P2)
001101
011010
100110
110010

XOR Gates

Y = P1 NAND P2 = (A NAND P0) NAND (P0 NAND B) = ((A NAND (A NAND B)) NAND ((B NAND (A NAND B))

XOR From NAND Truth Table

ABP0 (A NAND B)P1 (A NAND P0)P2 (P0 NAND B)Y (P1 NAND P2)
001110
011101
101011
110110

XNOR Gates

XNOR gates from NAND gates are basically negated XOR gates.

Y = P3 NAND P3 = (P1 NAND P2) NAND (P1 NAND P2) = ((A NAND P0) NAND (P0 NAND B)) NAND (A NAND P0) NAND (P0 NAND B) = (((A NAND (A NAND B)) NAND ((B NAND (A NAND B)) ) NAND (((A NAND (A NAND B)) NAND ((B NAND (A NAND B)))

XNOR From NAND Truth Table

ABP0 (A NAND B)P1 (A NAND P0)P2 (P0 NAND B)P3 (P1 NAND P2)Y (P0 NAND P0)
0011101
0111010
1010110
1101101
Logic Gates From NAND (NAND Logic)
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