This set practises Karnaugh map minimization for two, three and four variables. Questions cover grouping of adjacent cells, corner and edge wrap-around, don't-care conditions, prime and essential prime implicants, POS minimization and the basics of the Quine-McCluskey tabular method. It suits GATE preparation, university digital logic exams and interview rounds where you must simplify a function quickly and correctly.
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
- 3 and 4 variable K-map grouping
- Wrap-around and corner adjacency
- Don't-care conditions
- Prime and essential prime implicants
- POS minimization using zeros
- Quine-McCluskey tabular method
Digital Electronics MCQs with answers and explanations
Q1. The minimal SOP form of F(A,B,C) = Σm(0,1,2,3,6,7) is:
a) A' + AB
b) A + B'
c) B
d) A' + B
Q2. What is the minimal SOP of F(A,B,C,D) = Σm(0,2,8,10)?
a) A'B'
b) C'D'
c) B'D
d) B'D'
Q3. The function F(A,B,C,D) = Σm(1,3,5,7,9,11,13,15) reduces to:
a) C
b) A'D
c) CD
d) D
Q4. What is the minimal SOP for F(A,B,C,D) = Σm(4,5,6,7,12,13)?
a) A'B + BC'
b) BC'
c) A'B + ABC'
d) A'BC + BC'
Q5. Simplify F(A,B,C,D) = Σm(2,3,6,10,14) + d(7,11,15) using a K-map.
a) C
b) CD'
c) CD' + A'C
d) C + D'
Q6. How many prime implicants does F(A,B,C) = Σm(0,1,2,5,6,7) have?
a) 4
b) 6
c) 3
d) 5
Q7. A prime implicant is called essential when it:
a) covers at least one minterm that no other prime implicant covers
b) contains the largest number of minterms
c) includes at least one don't-care cell
d) has the fewest literals of all implicants
Q8. In a 4-variable K-map, a valid group of eight adjacent 1s yields a product term with how many literals?
a) 2
b) 1
c) 3
d) 8
Q9. In a 4-variable K-map (A as MSB), which cell is NOT logically adjacent to m5?
a) m6
b) m4
c) m7
d) m13
Q10. Why are the rows and columns of a K-map labelled in Gray code order?
a) To reduce the number of cells needed
b) So that physically adjacent cells differ in exactly one variable
c) To make the map self-complementing
d) Because minterms must be listed in decreasing order
Q11. In the Quine-McCluskey method, two implicants can be combined only when they:
a) have the same number of 1s
b) differ in at least two bit positions
c) differ in exactly one bit position and have dashes in the same positions
d) both contain a don't-care minterm
Q12. In the Quine-McCluskey method, combining the implicants 0101 and 0111 gives:
a) 0-01
b) 01-1
c) 01--
d) 011-
Q13. What is the minimal POS form of F(A,B,C) = ΠM(1,3,4,6)?
a) (A' + C')(A + C)
b) (A + B)C'
c) (A + C)(B' + C')
d) (A + C')(A' + C)
Q14. How are don't-care entries handled during K-map minimization?
a) They must always be treated as 1
b) They must always be treated as 0
c) Each one may be taken as 1 or 0, whichever gives a simpler result
d) They must be covered by an essential prime implicant
Q15. What is the minimal SOP of F(A,B,C,D) = Σm(0,3,4,7,8,11,12,15)?
a) C ⊕ D
b) A'B' + AB
c) C'D' + CD
d) C' + D
Q16. How many literals are in the minimal SOP of F(A,B,C,D) = Σm(0,1,2,3,4,5,6,7,8,9,10,11)?
a) 3
b) 4
c) 1
d) 2
Q17. Why does a K-map give no reduction for F(A,B,C) = Σm(1,2,4,7)?
a) The function has too many don't-care conditions
b) The function contains an essential prime implicant of size four
c) No two 1-cells are adjacent, so each minterm stays a separate 3-literal term
d) Three-variable maps cannot represent this function
Q18. What is the main practical advantage of the Quine-McCluskey method over K-maps?
a) It always needs fewer steps for 3-variable functions
b) It avoids the need to find prime implicants
c) It is systematic and easy to program for functions with many variables
d) It produces a POS form directly without any extra work
Quick revision notes
- A group of 2^k cells removes k variables from the term.
- Groups must be rectangular with sizes 1, 2, 4, 8 or 16; edges and corners wrap around.
- Gray code labels: 00, 01, 11, 10.
- Prime implicant: a group that cannot be enlarged; essential PI: covers a minterm no other PI covers.
- Use don't-cares only when they enlarge a group.
- POS: group the 0s and write sum terms (variable = 0 uncomplemented, = 1 complemented).
- Q-M: list minterms by count of 1s, combine terms differing in one bit, then use a prime implicant chart.
Frequently asked questions
What is the difference between a prime implicant and an essential prime implicant?
A prime implicant is an implicant that cannot be combined further into a larger group. It is essential only if it covers at least one minterm that no other prime implicant covers, so it must appear in every minimal solution.
Can a K-map give more than one minimal solution?
Yes. Functions with cyclic or overlapping prime implicants, such as Σm(0,1,2,5,6,7), can have several minimal covers with the same cost. Any of them is a correct answer.
When should you use Quine-McCluskey instead of a K-map?
Use Q-M when the function has more than four or five variables or when the minimization must be automated. For small hand problems a K-map is faster and less error-prone.
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