Gates and Circuits

1
Gates and Circuits
2
Three Main Gates

• AND
• OR
• NOT

3
NAND Gates

• NOT AND

4
Gate Diagrams

• Example MR S

5
Gate Diagrams

• Example

6
Gate Diagrams

• Example (MR S) (RS)

7
Gate Diagrams

• Exercise

8
Truth Table (to Expression) to Gates

• First, build the Boolean algebra expression that
  gives Z
• Z AB AB

9
Truth Table to Gates

• Z AB AB
• Next, build the circuit that goes with the
  Boolean algebra expression Z

10
Z AB AB
11
Boolean Expression to Gates

• Exercise
• (A B) A

12
Boolean Expression to Gates

• Exercise
• (A B) A

13
Multi-input AND and OR

• What circuit corresponds to ABC?
• ABC?

14
Binary Addition

• The first step in building our computer

15
Binary Addition
Sum
Carry
16
Binary Addition

17
Sum Circuit

Sum AB AB
18
Carry Circuit
Carry AB
19
Half Adder - Sum and Carry
20
Full Adder

21
4 Bit Adder

• Computers represent numbers in parallel.

22
Exercises

• Construct circuits with the following properties
  (using AND, OR or NOT gates)

23
Exercises

• A) B)

24
Exercises

• 2 - Fill in a truth table and give a Boolean
  expression for the following circuit.

25
Exercises

• 3 - How would you create a one binary digit
  multiplier? A two-digit by one-digit multiplier?