**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:**

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:**

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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