Boolean Expressions and Truth Tables - UNSOLVED PRACTICE SET
Chapter: Semiconductor Electronics | Topic: Boolean Expressions and Truth Tables
BOOLEAN EXPRESSIONS AND TRUTH TABLES - UNSOLVED PRACTICE SET
Topic: Boolean Expressions and Truth Tables
Multiple Choice Questions
Q1. In Boolean algebra, the complement of a variable A is represented as:
- A + 1
- Ā or A'
- A · 0
- 2A
Q2. According to De Morgan's theorem, (A + B)̄ is equal to:
- Ā + B̄
- Ā · B̄
- A · B
- A + B
Q3. The Boolean expression for an XOR gate is:
- A · B
- A + B
- A · B̄ + Ā · B
- Ā · B̄
Q4. The dual of a Boolean expression is obtained by:
- Replacing AND with OR, OR with AND, 0 with 1, and 1 with 0
- Replacing variables with their complements
- Replacing 0 with 1 only
- Replacing AND with NAND
Q5. The simplified form of the Boolean expression Y = A + Ā · B is:
- A · B
- A + B
- Ā + B
- A · B̄
Q6. A truth table for a logic circuit with n inputs has:
- n rows
- 2ⁿ rows
- n² rows
- 2n rows
Short Answer Questions
Q7. State the basic laws of Boolean algebra: commutative, associative, and distributive laws.
Q8. State De Morgan's theorems and verify one of them using a truth table.
Q9. What is the principle of duality in Boolean algebra? Give an example.
Q10. Simplify the Boolean expression: Y = A · B + A · B̄
Q11. Construct the truth table for the Boolean expression: Y = (A + B) · (Ā + B̄)
Q12. What is the difference between a minterm and a maxterm in Boolean algebra?
Long Answer Questions
Q13. State and prove De Morgan's theorems using truth tables. Show how these theorems are useful in simplifying Boolean expressions and designing logic circuits.
Q14. Explain the principle of duality in Boolean algebra with examples. Discuss how the dual of a Boolean expression is obtained and why this principle is useful.
Q15. Describe the process of simplifying Boolean expressions using Boolean algebra laws. Simplify the expression Y = A · B · C + A · B · C̄ + Ā · B · C + A · B̄ · C and draw the simplified logic circuit.
Numerical & Application-based Problems
Q16. Given the Boolean expression Y = Ā · B̄ · C + Ā · B · C̄ + A · B̄ · C̄ + A · B · C:
(a) Construct the complete truth table.
(b) Identify the minterms in this expression.
(c) Simplify the expression using Boolean algebra.
(d) Draw the logic circuit for both the original and simplified expressions.
Q17. Simplify the following Boolean expressions using Boolean algebra laws:
(a) Y = A + Ā · B
(b) Y = (A + B) · (A + C)
(c) Y = A · B + Ā · C + B · C
(d) For each simplified expression, draw the logic circuit using basic gates.
Q18. In your school computer science club, students are designing a digital voting system.
(a) Three students A, B, and C vote on a proposal. The proposal passes (output Y = 1) if at least two students vote YES. Write the Boolean expression for this system and construct the truth table.
(b) Simplify the Boolean expression using a Karnaugh map or Boolean algebra, and draw the simplified logic circuit.
(c) The student then designs a 2-bit comparator that outputs 1 when two 2-bit numbers A = A₁A₀ and B = B₁B₀ are equal. Write the Boolean expression and draw the circuit using XNOR and AND gates.
(d) A classmate suggests using a truth table with 16 rows to design a full adder (3 inputs, 2 outputs). Construct the truth table for a full adder and write the Boolean expressions for the sum and carry outputs.
(e) In India, digital systems are used in everything from Aadhaar authentication to railway signalling. Explain why Boolean simplification is crucial for designing efficient digital circuits, and how reducing the number of gates leads to faster, cheaper, and more reliable systems.