Logic Gates From NAND (NAND Logic)

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

A	Y (A NAND A)
0	1
1	0

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

A	B	P0 (A NAND B)	Y (P0 NAND P0)
0	0	1	0
0	1	1	0
1	0	1	0
1	1	0	1

OR Gates

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

OR From NAND Truth Table

A	B	P0 (A NAND A)	P1 (B NAND B)	Y (P0 NAND P1)
0	0	1	1	0
0	1	1	0	1
1	0	0	1	1
1	1	0	0	1

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

A	B	P0 (A NAND A)	P1 (B NAND B)	P2 (P0 NAND P1)	P2 (P2 NAND P2)
0	0	1	1	0	1
0	1	1	0	1	0
1	0	0	1	1	0
1	1	0	0	1	0

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

A	B	P0 (A NAND B)	P1 (A NAND P0)	P2 (P0 NAND B)	Y (P1 NAND P2)
0	0	1	1	1	0
0	1	1	1	0	1
1	0	1	0	1	1
1	1	0	1	1	0

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

A	B	P0 (A NAND B)	P1 (A NAND P0)	P2 (P0 NAND B)	P3 (P1 NAND P2)	Y (P0 NAND P0)
0	0	1	1	1	0	1
0	1	1	1	0	1	0
1	0	1	0	1	1	0
1	1	0	1	1	0	1