Boolean Algebra and its Simplification, Lecture notes of Digital Systems Design

Boolean algebra and de Morgan's theorem

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2019/2020

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LAB# 4
BAHRIA UNIVERSITY KARACHI CAMPUS
Department of Computer Science
DIGITAL LOGIC DESIGN
LAB EXPERIMENT # 4
APPLICATION OF BOOLEAN ALGEBRA
AND
DE MORGAN`S THEOREM
OBJECTIVE:-
Boolean algebra uses many of the same laws as those of ordinary algebra. De Morgan’s
theorem allows for the simplification of a Boolean Expression by the cancellation of
some redundant inversions. In this experiment, we’ll know about these laws & theorem.
EQUIPMENT:-
1. IC: 7400LS, 7404LS, 7408LS and 7432LS.
2. Bread board.
3. Connection Wires.
4. Digital Logic Probe.
5. DC supply (0 and +5V).
THEORY:-
Generally you’ll find that the basic logic functions AND, OR, NAND, NOR, and NOT
are not sufficient to implement complex digital logic functions. These gates are the basis
for building more complex logic circuits that are constructed using various combinations
of gates which is known as Combinational Logic. Combinational logic requires the use of
two or more gates to form a useful, complex function. These complex functions usually
begin as a Boolean Equation and the logic circuit may be implemented directly from this
equation. The Boolean laws and rules are shown below:
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BAHRIA UNIVERSITY KARACHI CAMPUS

Department of Computer Science

DIGITAL LOGIC DESIGN

LAB EXPERIMENT # 4

APPLICATION OF BOOLEAN ALGEBRA

AND

DE MORGAN`S THEOREM

OBJECTIVE:-

 Boolean algebra uses many of the same laws as those of ordinary algebra. De Morgan’s theorem allows for the simplification of a Boolean Expression by the cancellation of some redundant inversions. In this experiment, we’ll know about these laws & theorem. EQUIPMENT:-

  1. IC: 7400LS, 7404LS, 7408LS and 7432LS.
  2. Bread board.
  3. Connection Wires.
  4. Digital Logic Probe.
  5. DC supply (0 and +5V). THEORY:- Generally you’ll find that the basic logic functions AND , OR , NAND , NOR , and NOT are not sufficient to implement complex digital logic functions. These gates are the basis for building more complex logic circuits that are constructed using various combinations of gates which is known as Combinational Logic. Combinational logic requires the use of two or more gates to form a useful, complex function. These complex functions usually begin as a Boolean Equation and the logic circuit may be implemented directly from this equation. The Boolean laws and rules are shown below:

LAWS:-

Commutative property for addition A + B = B + A  Commutative property of multiplication A ● B = B ● A  Associative property of addition A + (B + C) = (A + B) + C  Associative property of multiplication A ● (B ● C) = (A ● B) ● C  Distributive property A ● (B + C) = (A + B) ● C

Figure# PROCEDURE:-

  1. At first construct the circuits shown in the Boolean laws.
  2. Check if the laws are valid. Give truth tables for each law.
  3. Construct the circuits shown in the circuit diagram.
  4. Check if the two circuits give the same result. OBSERVATION/RESULTS and DISCUSSION:-
  5. Write the truth table for Boolean Laws.
  6. Write the equation for the figure 1? Now try to simplify it and find the equation for figure 2 from it?
  7. Do it also by using Multisim. CONCLUSION:-  A circuit can easily represent in the form equation  It is easy to simplify the circuit using Boolean algebra.  After Simplification Hardware implantation is quite easy.  Truth table can easily be converted to Boolean expression and vice-versa.  Reduces the complexity. Teacher Signature : ________________________ Student Registration No. : ________________________