The document discusses basic logic gates used in digital design including NOT, AND, OR, NAND, NOR, and XOR gates. It provides truth tables that define the output of each gate based on the inputs. Specifically, it shows how the output is calculated for each type of gate and how NAND and NOR gates are functionally equivalent to NOT-AND and NOT-OR respectively.

1. Topic : Logic Gates

2. Basic Logic Gates
and Basic Digital Design
• NOT, AND, and OR Gates
• NAND and NOR Gates
• Exclusive-OR (XOR) Gate

3. NOT Gate -- Inverter
X Y
0
1
1
0

4. NOT
X ~X ~~X = X
X X X
0 1 0
1 0 1

5. OR Gate
OR
X
Y
Z
Z = X+Y
X Y Z
0 0 0
0 1 1
1 0 1
1 1 1

6. Basic Logic Gates
and Basic Digital Design
• NOT, AND, and OR Gates
• NAND and NOR Gates
• Exclusive-OR (XOR) Gate

7. NAND Gate
NAND
X
Y
Z
X Y Z
0 0 1
0 1 1
1 0 1
1 1 0
Z = (X & Y)

8. NAND Gate
NOT-AND
X
Y
Z
W = XY
Z = W = (X Y)
X Y W Z
0 0 0 1
0 1 0 1
1 0 0 1
1 1 1 0
W

9. NOR Gate
NOR
X
Y
Z
X Y Z
0 0 1
0 1 0
1 0 0
1 1 0
Z = (X+Y)

10. NOR Gate
NOT-OR
X
Y
X Y W Z
0 0 0 1
0 1 1 0
1 0 1 0
1 1 1 0
Z
W

11. Basic Logic Gates
and Basic Digital Design
• NOT, AND, and OR Gates
• NAND and NOR Gates
• Exclusive-OR (XOR) Gate

12. Basic Logic Gates
and Basic Digital Design
• NOT, AND, and OR Gates
• NAND and NOR Gates
• DeMorgan’s Theorem
• Exclusive-OR (XOR) Gate

13. Exclusive-OR Gate
X Y Z
XOR
X
Y
Z 0 0 0
0 1 1
1 0 1
1 1 0
Z = X ^ Y

14. Exclusive-NOR Gate
X Y Z
XNOR
X
Y
Z 0 0 1
0 1 0
1 0 0
1 1 1
Z = ~(X ^ Y)
Z = X ~^ Y
xnor(Z,X,Y)