D

NT

231

Digital

System

Semester 1 2008/2009

LAB

2

BOOLEAN THEOREMS

(De Morgan

‘s Theorem)

LECTURER

ASSO

C PROF DR

KENNETH SUDARAJ

PLV

MRS

FARI

DAH HASSAN

TECHNICIAN

MR BAZLI BAHADON

Student’s Particular:

Name

Matrix No

.

Programme

Group

Date

of exp.

Received by

:______________

Date

:______________

MARKS

LAB

2

:

BOOLEAN THEOREMS

(De Morgan

‘s Theorem)

OBJECTIVES

1.

To implement DeMorgan's theorems in circuit simplification.

2.

To design a combinational logic circuit with simplest l

ogic gates representation

using Karnaugh Mapping Technique.

EQUIPMENTS/COMPONENTS

A DC power supply capable of 5V DC output

A multimeter

Logic

Gate IC :

7404 (1pc), 7432 (1pc), 7408 (1pc)

Light Emitting Diode (1

pc)

Resistors : 330Ω

(1

pc)

Switches (2

pc

s

)

INTRODUCTION

Boolean algebra is the mathematics of digital systems. A basic knowledge of Boolean

algebra is indispensable to the study and analysis of logic circuits.

Theorems of Boolean Algebra are a set of rules used with digital variables and logical

operations to develop, manipulate and simplify logical expressions.

De

Morgan Theorems

De Morgan's theorem allows large bars in a Boolean expression to be broken up into

smaller bars over individual variables. De Morgan's theorem says that a large bar

over

several variables can be broken between the variables if the sign between the variables is

changed.

DeMorgan’s theorems is stated as follows :

The complement of two or more ANded variables is equivalent to the OR of the

complements of the individual

variables.

The formula for expressing this theorem for two variables is ;

AB = A + B

DeMorgan’s second theorem is stated as follows :

The complement of two or more Red Variable is equivalent to the AND of the

complements of the individual variable

s.

The formula for expressing this theorem for two variables is ;

A+B = A B

For this session, you will implement De Morgan Theorem into a given Boolean Equation.

PROCEDURE

1.

Draw a logic diagram for the equation :

2.

Construct the circuit using the

diagram you drew in Step 1. Connect toggle switches

to inputs A, B and a LED to the circuit output, Y. Set the toggle switches to each

input combination listed in Table 2.1, and record the output value observed in the

table.

3.

Apply De Morgan’s laws to remov

e the top inversion bar by changing the sign. Get

the simplified expression and draw the logic circuit diagram in the space given below:

4.

Construct a logic circuit for the simplified expression obtained in step 3 and again

complete the truth table in Table

2

.

2

.

RESULT

1)

Draw logic circuit diagram for

:

Y= A + B

Y= A + B

2)

Simplification Using De Morgan Theorem

& draw the respective logic circuit

diagram

Y=

3)

Complete table below:

inputs

outputs

inputs

outputs

Table 2.1 : Step 1 Operation

Table 2.2 : Step 3 Operation

CONCLUSION

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