Rules of Boolean algebra for simplification

Boolean algebra is a very useful method for the simplification of binary expressions. There is no connection between known general algebra and Boolean algebra. Boolean algebra deals with the binary bits only. There are different laws of Boolean algebra to simplify Boolean expressions. In this article, we are going to discuss all rules of Boolean algebra for the simplification of Boolean functions.

Rules of Boolean algebra

Let A, B, C…. etc. be the binary bits. Then the laws of Boolean algebra to simplify binary equations consist of these binary bits and their complements are as followings-

Addition rule

1+A = 1

1+ $\small \bar{A}$ = 1
A+ $\small \bar{A}$ = 1
A+ $\small \bar{A}$ B = A+B

Multiplication rule

A.A = A
A. $\small \bar{A}$ = 0
AB = BA

Karnaugh Map is another method for simplification of Boolean equations. Students find this method easier than Boolean and de Morgan’s method.

Examples of simplification of Boolean expression by Boolean algebra

1. Simplify the binary expression using Boolean algebra: $\small {\color{Red} Y = (AB + A\bar{B} + C)}$ .

Answer:

\small {\color{blue} Y = (AB + A\bar{B} + C)}

or, $\small {\color{Blue} Y = A(B+\bar{B})+C}$

Then, $\small {\color{Blue} Y = A+C}$

This is the simplified form of the Boolean expression.

2. Simplify the Boolean expression $\small {\color{Red} Y = (1 + A\bar{B} + B)}$ by using Boolean algebra.

Answer:

\small {\color{blue} Y = AB + A\bar{B} + C}

or, $\small {\color{Blue} Y= 1 + A + B}$ . [ Since, $\small A\bar{B}$ +B = A+B ]

or, $\small {\color{Blue} Y= 1 + B}$ . [ Since, 1+A = 1].

or, $\small {\color{Blue} Y= 1 }$ .

These are the rules for simplification of Boolean algebra in digital electronics. This is all from this article. If you have any further queries you can ask me in the comment section.

Thank you!

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Karnaugh map for simplification of Boolean expressions