Rules of Boolean algebra for simplification

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Boolean algebra is the mathematical reasoning for simplification of binary expressions. It is completely different from the conventional general algebra. Boolean algebra deals with the binary bits only which is the arithmatic method of computers. There are different laws of Boolean algebra that are used to simplify Boolean expressions. In this article, we are going to discuss all these rules of Boolean algebra with examples.

Rules of Boolean algebra

There are mainly two rules in Boolean algebra – Addition rule and Multiplication rule. Let A, B, C…. etc. are the variables that represent binary bits 0 or 1.

Boolean addition rule

  1. 1+A = 1
  2. 1+\small \bar{A} = 1
  3. A+\small \bar{A} = 1
  4. A+\small \bar{A}B = A+B

Boolean multiplication rule

  1. A.A = A
  2. A.\small \bar{A} = 0
  3. AB = BA

Karnaugh Map is another method for simplification of Boolean equations that can be an easier method 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!

Related Posts:

  1. Karnaugh map for simplification of Boolean expressions
  2. Basic logic gates
  3. XOR gate using NAND gate

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