1. Chapter 2 Gates

2. 2019/2/27
Binary Logic
Deals with binary variables that take 2 discrete values (0 and 1), and with logic operations
Three basic logic operations:
AND, OR, NOT
Binary/logic variables are typically represented as letters: A,B,C,…,X,Y,Z
Boolean Algebra
2019/2/27
Boolean Algebra

3. NOT Gate -- Inverter X Y 1 1

4. AND Gate
AND
X Y Z X Z Y
Z = X & Y

5. OR Gate OR
X Y Z X Z Y
Z = X | Y

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

7. NAND Gate
NAND
X Y Z X Z Y

8. NAND Gate
NOT-AND
X Y W Z X W Z Y

9. NOR Gate
NOR
X Y Z X Z Y

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

11. NAND Gate X X Z Z = Y Y
X Y W Z
X Y ~X ~Y Z

12. NOR Gate X X Z Z Y Y X Y Z X Y ~X ~Y Z 0 0 1 0 0 1 1 1 0 1 0 0 1 1 0 0
X Y ~X ~Y Z

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

14. Exclusive-NOR Gate
XNOR
X Y Z X Z
0 0 1 Y
0 1 0
1 0 0
1 1 1

15. Multiple-input AND GateZ 1
Output is HIGH only if all inputs are HIGH Z 1
An open input will float HIGH

16. Multiple-input OR GateZ 2
Output is LOW only if all inputs are LOW Z 2

17. Multiple-input NAND GateZ 3
Output is LOW only if all inputs are HIGH Z 3

18. Multiple-input NOR GateZ 4
Output is HIGH only if all inputs are LOW Z 4

19. Universal Gates
Proving NAND gate is universal

20. NOR Gate (Universal)
Proving NOR gate is universal

21. Logic Chips (cont.) Integration levels SSI (small scale integration)
Introduced in late 1960s
1-10 gates (previous examples)
MSI (medium scale integration)
gates
LSI (large scale integration)
Introduced in early 1970s
100-10,000 gates
VLSI (very large scale integration)
Introduced in late 1970s
More than 10,000 gates

22. Logic Design 3-input majority function A B C F 0 0 0 0 0 0 1 0 0 1 0 0
Logical expression form
F = A B + B C + A C