Question

How do you start an analysis and simplification using Boolean Algebra? Give a strategy for beginning such a problem.

Answer 1

INTRODUCTION

It is a division of mathematics that deals with logical operation. Boolean algebra variables are presented with the possible values are  1 ( TRUE ) or 0 ( FALSE ) . Boolean algebra is a process to analyze digital logic circuit. It can be understand only binary digit i.e. 0 or 1. It is also called binary algebra or logical algebra. It was invented by george boole in 1854.

We can use boolean algebra for simplificationlogic circuits. It helps to translate logic circuits into boolean form and apply some algebric operation. Herae are some rules for simplification to solve boolean expression.

• The Idempotent Laws

XX = X

X+X = X

• The Associative Laws

(XY)Z = X(YZ)

(X+Y)+Z = X+(Y+Z)

• The Commutative Laws

XY = YX

X+Y = Y+X

• The Distributive Laws

X(Y+Z) = XY+XZ

X+YZ = (X+Y)(X+Z)

• The Identity Laws

XF = F

XT = X

X+F = X

X+T = T

• The Complement Laws

XX = F

X+X = T

F = T

T = F

• The Involution Law

X = X

• DeMorgan's Law

XY = X+Y

X+Y = X Y