---
title: "Short note: Boolean algebra"
subject: "Basic Electrical and Electronics Engineering"
chapter: 3
key: "semester_1/basic_electrical_and_electronics_engineering:short-note-boolean-algebra"
source: https://www.bctengineer.com/q/semester_1/basic_electrical_and_electronics_engineering/short-note-boolean-algebra
site: BCT Engineering
---

# Short note: Boolean algebra

Basic Electrical and Electronics Engineering · Chapter 3: Introduction to Electronics Engineering

- Asked in: 2081 Kartik (new course), 3 marks
- Video: [Boolean Algebra Basics and Example Problem](https://www.youtube.com/watch?v=jDnni-zm2g8) — Tangerine Code
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_1/basic_electrical_and_electronics_engineering/short-note-boolean-algebra
- Whole chapter: https://www.bctengineer.com/md/semester_1/basic_electrical_and_electronics_engineering/chapter-3

## Question

Write a short note on Boolean Algebra.

## Short answer

Boolean algebra, developed by George Boole, deals with binary variables (0,1) and operations AND, OR, NOT. It simplifies logic circuits using laws like commutativity, distributivity, and De Morgan's theorems (e.g., (A·B)' = A' + B') to reduce gate count.

## Answer

Boolean algebra, developed by George Boole, is the algebra of binary variables (0 and 1) with the operations AND (·), OR (+) and NOT (bar). It is used to describe and simplify digital logic circuits, so that fewer gates are needed.

**Basic laws and identities:**

| Law | AND form | OR form |
|---|---|---|
| Identity | $A\cdot1=A$ | $A+0=A$ |
| Null | $A\cdot0=0$ | $A+1=1$ |
| Idempotent | $A\cdot A=A$ | $A+A=A$ |
| Complement | $A\cdot\bar A=0$ | $A+\bar A=1$ |
| Commutative | $AB=BA$ | $A+B=B+A$ |
| Associative | $(AB)C=A(BC)$ | $(A+B)+C=A+(B+C)$ |
| Distributive | $A(B+C)=AB+AC$ | $A+BC=(A+B)(A+C)$ |
| Absorption | $A(A+B)=A$ | $A+AB=A$ |

Also, double negation: $\bar{\bar A}=A$.

**De Morgan's theorems:**

$$
\overline{A\cdot B}=\bar A+\bar B, \qquad \overline{A+B}=\bar A\cdot\bar B
$$

**Example of simplification:**

$$
Y=AB+A\bar B=A(B+\bar B)=A\cdot1=A
$$

Boolean expressions can be written in sum-of-products or product-of-sums form, and further simplified using Karnaugh maps.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What is the main use of Boolean algebra in digital design?
   A. To calculate analog voltages
   B. To describe and simplify logic circuits so fewer gates are needed
   C. To increase the number of gates in a circuit
   D. To convert decimal numbers to hexadecimal only
   Answer: B. It describes digital logic and simplifies expressions, reducing the gates required. (Key point: Purpose of Boolean algebra)

2. According to De Morgan's theorem, what is the complement of (A + B)?
   A. A' + B'
   B. A' . B'
   C. A . B
   D. (A . B)'
   Answer: B. The complement of A+B equals A' . B' (NOR equals AND of complements). (Key point: De Morgan's theorem)

3. How does Y = AB + AB' simplify?
   A. Y = B
   B. Y = A + B
   C. Y = A
   D. Y = 1
   Answer: C. Y = A(B + B') = A . 1 = A, using the complement and identity laws. (Key point: Simplification)

## Related in other subjects

- [Commutative and associative laws; A+A'B = A+B](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Aboolean-laws-simplify) — Digital Logic, chapter 2