This set focuses on Boolean algebra and logic gates. You will apply Boolean laws, De Morgan's theorem, consensus and duality, build functions from NAND and NOR universal gates, and move between SOP, POS, minterm and maxterm forms. It is useful for GATE, university semester exams in digital logic design and technical interview rounds where quick algebraic simplification is expected.
How to practise: read each question and tap the option you think is correct. You will see right away whether you got it, along with a short explanation, and your score is tracked at the bottom of the screen. This set has 18 questions.
Topics covered in this set
- Boolean laws, absorption and consensus
- De Morgan's theorem and complements
- Duality and self-dual functions
- NAND and NOR as universal gates
- XOR and XNOR properties
- Canonical SOP and POS forms
- Minterms and maxterms
Digital Electronics MCQs with answers and explanations
Q1. The Boolean expression A + A'B simplifies to which of the following?
a) AB
b) A + B
c) A
d) B
Q2. By De Morgan's theorem, the complement of the product ABC equals which expression?
a) A' + B' + C'
b) A'B'C'
c) (A + B + C)'
d) A + B + C
Q3. What is the minimum number of 2-input NAND gates needed to implement a 2-input XOR gate?
a) 5
b) 3
c) 6
d) 4
Q4. What is the minimum number of 2-input NOR gates needed to realise a 2-input AND function?
a) 2
b) 3
c) 4
d) 5
Q5. The expression AB + A'C + BC simplifies to which of the following?
a) AB + BC
b) A'C + BC
c) AB + A'C
d) AB + A'C + C
Q6. The function F(A,B,C) = Σm(1,3,5,7), with A as the MSB, reduces to which expression?
a) A
b) A'C
c) B + C
d) C
Q7. How many distinct Boolean functions can be defined on 3 input variables?
a) 64
b) 8
c) 512
d) 256
Q8. What is the dual of the expression A(B + C')?
a) A' + B'C
b) A'(B' + C)
c) A + BC'
d) (A + B)C'
Q9. What is the complement of F = AB' + C?
a) (A' + B)C'
b) A'B + C'
c) A' + B + C'
d) A'BC'
Q10. For three variables A, B, C with A as the MSB, which expression is the maxterm M5?
a) AB'C
b) A + B' + C
c) A' + B + C'
d) A'BC'
Q11. The function F(A,B,C) = Σm(0,2,4,6) is equivalent to which product of maxterms?
a) ΠM(1,3,5,7)
b) ΠM(0,2,4,6)
c) ΠM(1,3,5)
d) ΠM(1,3,6,7)
Q12. What is the value of A ⊕ A ⊕ A ⊕ A'?
a) 0
b) A
c) 1
d) A'
Q13. The output of a 2-input XNOR gate is 1 when:
a) exactly one input is 1
b) both inputs are equal
c) both inputs are 1 only
d) at least one input is 0
Q14. Which gate produces a 1 at its output only when all of its inputs are 0?
a) NOR
b) NAND
c) XNOR
d) AND
Q15. How many minterms appear in the canonical SOP form of F(A,B,C) = A + B'C?
a) 6
b) 4
c) 5
d) 3
Q16. The expression (A + B)(A + B') simplifies to:
a) B
b) A
c) AB
d) 1
Q17. Which of the following functions is self-dual?
a) A + B
b) AB + BC + CA
c) AB
d) A ⊕ B
Q18. How many 2-input NAND gates are needed to implement F = AB + CD directly in two-level form?
a) 4
b) 5
c) 2
d) 3
Quick revision notes
- Absorption: A + AB = A and A(A + B) = A.
- A + A'B = A + B; A(A' + B) = AB.
- Consensus: AB + A'C + BC = AB + A'C.
- De Morgan: (AB)' = A' + B'; (A + B)' = A'B'.
- NAND and NOR are universal; XOR needs 4 NANDs or 5 NORs.
- Number of Boolean functions of n variables = 2^(2^n).
- Minterm m(i) is 1 only for row i; maxterm M(i) is 0 only for row i; Σm and ΠM use complementary index sets.
- Duality swaps AND/OR and 0/1 without complementing variables.
Frequently asked questions
Why are NAND and NOR gates called universal gates?
Any Boolean function can be built using only NAND gates or only NOR gates, because each can produce NOT, AND and OR. This simplifies IC manufacturing since a single gate type suffices.
What is the difference between a minterm and a maxterm?
A minterm is a product of all variables that equals 1 for exactly one input combination, while a maxterm is a sum of all variables that equals 0 for exactly one combination. Canonical SOP uses minterms and canonical POS uses maxterms.
What is the difference between the dual and the complement of a Boolean expression?
The dual interchanges AND with OR and 0 with 1 but leaves variables unchanged. The complement does the same interchange and also complements every variable, producing the logical inverse of the function.
Comments
Post a Comment