The Islamic University of Gaza

Engineering Faculty

Department of Computer Engineering

Fall 2018

ECOM 2013

Eng. Abdelrahman M. Hamada Eng. Aya Samour

Combinational Digital Design

Laboratory Manual

2

Objectives

• To study Basic logic gates: INV, AND, OR, NAND, NOR, XOR, XNOR

• To study Logic Diagrams, Boolean Functions, Truth Tables and Boolean algebra of these

gates.

Prelab

Use Logisim Software to simulate the functions of the basic gates as shown in figures below.

Theoretical Background

1. Inverter Gate (NOT)

• Logic Diagram

• Truth Table

Input Output

0 1

1 0

• Boolean Expression F = A'

• Pin Diagram

2. AND Gate

• Logic Diagram

3

• Truth Table

Input1 Input2 Output

0 0 0

0 1 0

1 0 0

1 1 1

• Boolean Expression F = AB = A . B

• Pin Diagram

3. OR Gate

• Logic Diagram

• Truth Table

Input1 Input2 Output

0 0 0

4

0 1 1

1 0 1

1 1 1

• Boolean Expression F = A + B

• Pin Diagram

4. NAND Gate

• Logic Diagram

• Truth Table

Input1 Input2 Output

0 0 1

0 1 1

1 0 1

1 1 0

• Boolean Expression F = (AB)' = A' + B'

• Pin Diagram

5

5. NOR Gate

• Logic Diagram

• Truth Table

Input1 Input2 Output

0 0 1

0 1 0

1 0 0

1 1 0

• Boolean Expression F = (A + B)' = A'B'

• Pin Diagram

6

6. XOR Gate

• Logic Diagram

• Truth Table

Input1 Input2 Output

0 0 0

0 1 1

1 0 1

1 1 0

• Boolean Expression

F = A B = A'B + AB'

• Pin Diagram

7. XNOR Gate

• Logic Diagram

• Truth Table

Input1 Input2 Output

7

0 0 1

0 1 0

1 0 0

1 1 1

• Boolean Expression

F = (A B)' = (A + B')(A' + B)

Examples on Boolean Algebra

Example 1: Using Logisim, draw a circuit that uses basic logic gates to realize the following

function

F = AB' + C

Solution:

Example 2: Write Boolean expression describing the output of the circuit described by the

logic diagram in the Figure below

8

Solution:

F = (AB + C)' D

DE Morgan's Theorem

• (XY)' = X' + Y'

• (X + Y)' = X'Y'

• Truth Table for DE Morgan's Theorem:

X Y X' Y' X + Y (X + Y)' X'Y' XY (XY)' X' + Y'

0 0 1 1 0 1 1 0 1 1

0 1 1 0 1 0 0 0 1 1

1 0 0 1 1 0 0 0 1 1

1 1 0 0 1 0 0 1 0 0

Lab Work

Equipment’s required:

• KL-31001 trainer kit.

• IC's 74LS04 (Hexa NOT), 74LS08 (Quad 2 input AND), 74LS32 (Quad 2 input OR).

• The Datasheets of the IC’s.

9

Basic Gates

• Connect the 74LS08 to the breadboard, connect +5V to pin 14 and 0V (ground) to pin

7, connect one AND gate inputs to data switches, SW1 and SW2 TTL level and output to

LED L0 of the trainer kit, and record down its truth table.

• Repeat previous part for all other gates.

Exercises

1. Using Logisim:

a. Build INV gate using a single 2-input NAND gate.

b. draw logic diagram for the following expression:

u + w(xyz)'

2. Write Boolean expression and construct the truth table describing the output of the

circuit described by the logic diagram in the Figure below.