CS302 Lab Manual Week 4

Lab Experiment # 04

Boolean algebra and Simplification of Boolean expressions - I

Objectives

Object

1To study DE Morgan’s theory and implemented it. 2Learn how to simplify Boolean logic equations using DE Morgan’s theory.

DE Morgan’s Theory – Background

Augustus De Morgan (27 June 1806 – 18 March 1871) was a British mathematician and logician. He formulated De Morgan's laws. In simple words, DE Morgan’s Theory is used to convert AND/NAND gates to OR/NOR ones, and presented OR/NOR gates by AND/NAND gates by these 2-laws: A + B= (A’. B’)’

A. B = (A’ + B’)’

Basics of Boolean algebra

Boolean Postulates

P1: X = 0 or X = 1 P2: 0. 0 = 0 P3: 1 + 1 = 1 P4: 0 + 0 = 0 P5: 1. 1 = 1 P6: 1. 0 = 0. 1 = 0 P7: 1 + 0 = 0 + 1 = 1

Task 3: Simplifying Boolean functions

Simplify the following Boolean expression F (A, B) = (A. B) + A’ (A+B)

Draw the simplified and the original Boolean expression using EWB and make sure that they are booth equivalent by filling-in the following truth table. A B F (A, B) (original) Y (Simplified)

Task 4: Simplifying Boolean functions

Simplify the following Boolean expression F (A, B, C) = (A+C’) + C (C.A’ + (B.A) +C

Draw the simplified Boolean expression using EWB. Find out the truth table of the circuit.