DNT 231
Digital System
Semester 1 2008/2009
LAB 2
BOOLEAN THEOREMS
(De Morgan‘s Theorem)
LECTURER
ASSOC PROF DR KENNETH SUDARAJ
PLV
MRS FARIDAH 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 logic gates representation
using Karnaugh Mapping Technique.
EQUIPMENTS/COMPONENTS
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A DC power supply capable of 5V DC output
A multimeter
Logic Gate IC : 7404 (1pc), 7432 (1pc), 7408 (1pc)
Light Emitting Diode (1pc)
Resistors : 330Ω (1pc)
Switches (2pcs)
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 variables.
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 :
Y= A + B
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 remove 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
2) Simplification Using De Morgan Theorem & draw the respective logic circuit
diagram
Y=
3) Complete table below:
inputs
outputs
Table 2.1 : Step 1 Operation
CONCLUSION
inputs
outputs
Table 2.2 : Step 3 Operation