🔷 For UPP SI, UP Police, SSC, RRB, RRB NTPC, BPSC and other government exams.
📘 Boolean Algebra – Complete Study Notes
🔹 Introduction
Boolean Algebra is a branch of mathematics used in computer science and digital electronics. It deals with binary variables (0 and 1) and logical operations.
It was introduced by
👉 George Boole
🔹 Basic Terms in Boolean Algebra
| Term | Meaning |
|---|---|
| Binary Numbers | Only 0 and 1 |
| Variable | A symbol representing value (A, B, X) |
| Complement | Opposite value (A' or NOT A) |
| Logic Gates | Electronic circuits (AND, OR, NOT) |
🔹 Basic Boolean Operations
1. AND Operation (·)
Symbol: A · B
Output is 1 only when both inputs are 1
| A | B | A·B |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
2. OR Operation (+)
Symbol: A + B
Output is 1 if any input is 1
| A | B | A+B |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 1 |
3. NOT Operation (')
Symbol: A'
Output is opposite of input
| A | A' |
|---|---|
| 0 | 1 |
| 1 | 0 |
🔹 Important Boolean Laws
1. Identity Law
A + 0 = A
A · 1 = A
2. Null Law
A + 1 = 1
A · 0 = 0
3. Idempotent Law
A + A = A
A · A = A
4. Complement Law
A + A' = 1
A · A' = 0
5. Commutative Law
A + B = B + A
A · B = B · A
6. Associative Law
(A + B) + C = A + (B + C)
(A · B) · C = A · (B · C)
7. Distributive Law
A · (B + C) = A·B + A·C
A + (B · C) = (A + B)(A + C)
🔹 De Morgan’s Theorem (Very Important)
(A · B)' = A' + B'
(A + B)' = A' · B'
👉 Used in simplifying logical expressions
🔹 Boolean Expression Example
Simplify:
A + A·B
Solution:
= A (1 + B)
= A
🔹 Applications of Boolean Algebra
Digital Circuits
Computer Programming
Logic Gates Design
Switching Circuits
Database Queries
📝 20 Important MCQs on Boolean Algebra
1. Boolean Algebra deals with:
A) Decimal numbers
B) Binary numbers ✅
C) Fractions
D) Algebraic equations
2. Who invented Boolean Algebra?
A) Newton
B) Einstein
C) George Boole ✅
D) Pascal
3. A + 0 = ?
A) 0
B) 1
C) A ✅
D) A'
4. A · 1 = ?
A) 1
B) A ✅
C) 0
D) A'
5. A + A = ?
A) 2A
B) A ✅
C) 0
D) 1
6. A · 0 = ?
A) A
B) 1
C) 0 ✅
D) A'
7. A + 1 = ?
A) 0
B) A
C) 1 ✅
D) A'
8. Complement of 1 is:
A) 1
B) 0 ✅
C) 2
D) None
9. NOT gate gives:
A) Same output
B) Opposite output ✅
C) Random output
D) No output
10. AND gate output is 1 when:
A) Both inputs are 0
B) Any input is 1
C) Both inputs are 1 ✅
D) None
11. OR gate output is 0 when:
A) Both inputs are 0 ✅
B) One input is 1
C) Both inputs are 1
D) None
12. A + A' = ?
A) 0
B) A
C) 1 ✅
D) A²
13. A · A' = ?
A) 1
B) 0 ✅
C) A
D) A'
14. (A + B)' = ?
A) A' + B'
B) A' · B' ✅
C) AB
D) None
15. (A · B)' = ?
A) A' + B' ✅
B) A'B'
C) AB
D) None
16. Boolean Algebra is used in:
A) Cooking
B) Digital Electronics ✅
C) Farming
D) Drawing
17. Binary system uses:
A) 0–9
B) 1–10
C) 0 and 1 ✅
D) None
18. A · (B + C) = ?
A) AB + AC ✅
B) A + B + C
C) ABC
D) None
19. A + (B · C) = ?
A) (A + B)(A + C) ✅
B) AB + AC
C) ABC
D) None
20. Boolean Algebra is important for:
A) Painting
B) Circuit Design ✅
C) Music
D) Sports
🔥 Very Important Topics: Must see
✅ Social Media Networking
✅ Cyber Crime and Security
✅ Open Education Resources (OER)
✅ E-commerce and Internet
✅ Important files extension names
