Boolean Algebra Notes, Formulas & Concepts – GATE CSE Digital Logic

Boolean Algebra Notes & Formulas

Generate GATE-level questions covering Boolean identities, De Morgan’s laws, simplification of expressions, canonical forms (SOP/POS), and equivalence transformations. Include tricky simplification and expression evaluation problems.

Concept summary for GATE CSE 2027 · 195 practice questions available

📘 Boolean Algebra – Concept Summary

1. Definition

Mathematical structure for binary variables and logical operations. Variables take values 0 or 1 only.

2. Core Laws (Very Important)

| Law | AND form | OR form |
|---|---|---|
| Identity | A·1 = A | A+0 = A |
| Null | A·0 = 0 | A+1 = 1 |
| Idempotent | A·A = A | A+A = A |
| Complement | A·A' = 0 | A+A' = 1 |
| Absorption | A·(A+B) = A | A+(A·B) = A |
| De Morgan's | (A·B)' = A'+B' | (A+B)' = A'·B' |

3. De Morgan's Theorem (Very Important)

(A·B)' = A' + B' → Break the bar, change the operator
(A+B)' = A'·B'
Works for any number of variables

4. Duality Principle

Every Boolean expression remains valid if AND↔OR and 0↔1 are swapped simultaneously.

5. Consensus Theorem

AB + A'C + BC = AB + A'C (BC is redundant)
Dual: (A+B)(A'+C)(B+C) = (A+B)(A'+C)

6. Key Points

Boolean algebra follows Huntington's postulates
Complement is unique for every element
Precedence: NOT > AND > OR

7. GATE Trick

Simplification questions: apply absorption and De Morgan's first - they give maximum reduction fastest. Consensus theorem removes a term without introducing new variables.