The Islamic University of Gaza
Engineering Faculty
Department of Computer Engineering
Fall 2017
ECOM 2013
Lamia Z. Shu'shaa
Khaleel I. Shaheen
Combinational Digital Design
Laboratory Manual
Experiment #1
Basic Logic Functions & Gates
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
•
Boolean Expression
F = A'
•
2
Pin Diagram
Input
Output
0
1
1
0
2. AND Gate
•
Logic Diagram
•
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
•
3
Logic Diagram
•
•
Truth Table
Input1
Input2
Output
0
0
0
0
1
1
1
0
1
1
1
1
Input1
Input2
Output
0
0
1
0
1
1
1
0
1
1
1
0
Boolean Expression
F=A+B
•
Pin Diagram
4. NAND Gate
4
•
Logic Diagram
•
Truth Table
•
Boolean Expression
F = (AB)' = A' + B'
•
Pin Diagram
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'
•
5
Pin Diagram
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'
•
6
Pin Diagram
7. XNOR Gate
•
Logic Diagram
•
Truth Table
•
Input1
Input2
Output
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:
7
Example 2: Write Boolean expression describing the output of the circuit described by the
logic diagram in the Figure below
Solution:
F = (AB + C)' D
DE Morgan's Theorem
8
•
(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.
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, 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.
9