Phase 4 Checkpoint: 15 questions on K-maps, prime implicants, don't-cares and the tabular method.
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15 questions · 23 marks · 45 minutes. Negative marking on MCQ only: −1/3 mark for a wrong 1-mark MCQ, −2/3 for a wrong 2-mark MCQ. No negative marking for MSQ or NAT; MSQ has no partial credit.
Q1MCQ1 markLayout
In a 4-variable K-map (AB rows, CD columns), which cell is in row AB = 11, column CD = 10?
- (A) 14
- (B) 13
- (C) 15
- (D) 10
Q2NAT1 markGroup
A group in a 4-variable K-map covers 16 cells. What is its term? Give the number of literals.
Numerical answer: ________
Q3MCQ2 marksMinimise
F(A, B, C) = Σm(0, 1, 2, 3, 7). The minimal SOP is:
- (A) A' + ABC
- (B) A'B' + A'B + BC
- (C) A + BC
- (D) A' + BC
Q4NAT2 marksMinimise
F(A, B, C, D) = Σm(0, 2, 8, 10, 4, 12). How many literals in the minimal SOP?
Numerical answer: ________
Q5NAT2 marksPIs
F(A, B, C, D) = Σm(0, 4, 5, 7, 8, 9, 13, 15). How many prime implicants does it have?
Numerical answer: ________
Q6NAT2 marksMinimal
F(A, B, C, D) = Σm(0, 4, 5, 7, 8, 9, 13, 15). How many literals are in the minimal SOP?
Numerical answer: ________
Q7MCQ1 markRedundant
F = Σm(1, 5, 6, 7, 11, 12, 13, 15). The prime implicant BD:
- (A) must be used twice
- (B) is not prime
- (C) is prime but not needed in the minimal SOP
- (D) is essential
Q8MCQ2 marksPOS
The minimal POS of F(A, B, C, D) = Σm(2, 3, 5, 7, 8, 9, 10, 11, 13, 15) is:
- (A) (B + C)(A + D)
- (B) (A + B + C)(B' + D)
- (C) (A + C)(B' + D)
- (D) (A' + B' + C')(B + D')
Q9NAT2 marksCyclic
F(A, B, C) = Σm(0, 1, 2, 5, 6, 7). How many literals in a minimal SOP?
Numerical answer: ________
Q10NAT2 marksDon't-care
F(A, B, C, D) = Σm(4, 5, 6, 7, 8, 9) + d(10, 11, 12, 13, 14, 15). How many literals in the minimal SOP?
Numerical answer: ________
Q11MCQ1 markDon't-care
In K-map minimisation, a don't-care cell:
- (A) may be grouped if it helps make a larger group
- (B) must be grouped
- (C) is counted when deciding essential PIs
- (D) is always 0
Q12NAT2 marksFive variables
In a 5-variable function, a prime implicant has the term BD'E. How many minterms does it cover?
Numerical answer: ________
Q13MCQ1 markTabular
In the Quine–McCluskey method, the prime implicants are:
- (A) the terms in the last column only
- (B) all terms that were never ticked
- (C) all minterms with an odd number of 1s
- (D) the terms in the first column
Q14NAT1 markMerge
Merging 1-00 and 1-10 gives a term with how many dashes?
Numerical answer: ________
Q15MCQ1 markDon't-care in QM
In the tabular method, don't-cares are:
- (A) ignored completely
- (B) treated as 0
- (C) used in merging but not listed as chart columns
- (D) listed as chart columns but not merged
✓Answer Vault
Answer Vault
Try the questions first. Open when you are ready to check.
Q1 Answer: (A)1 mark
- (B) is wrong: Column 01.
- (C) is wrong: Column 11.
- (D) is wrong: Row 10.
Re-read: Lesson 4.1.1 — Karnaugh maps for 2, 3 and 4 variables: adjacency and grouping
Q2 Answer: 01 mark
The whole map: F = 1.
Re-read: Lesson 4.1.1 — Karnaugh maps for 2, 3 and 4 variables: adjacency and grouping
Q3 Answer: (D)2 marks
The whole A = 0 row plus 3, 7.
- (A) is wrong: ABC is not prime (BC is larger).
- (B) is wrong: Not minimal.
- (C) is wrong: Row A = 1 is mostly 0s.
Re-read: Lesson 4.1.1 — Karnaugh maps for 2, 3 and 4 variables: adjacency and grouping
Q4 Answer: 42 marks
C'D' + B'D'.
Re-read: Lesson 4.1.1 — Karnaugh maps for 2, 3 and 4 variables: adjacency and grouping
Q5 Answer: 62 marks
A'C'D', B'C'D', A'BC', AB'C', AC'D, BD.
Re-read: Lesson 4.1.2 — Prime implicants, essential prime implicants, minimal SOP and POS
Q6 Answer: 82 marks
BD + A'C'D' + AB'C'.
Re-read: Lesson 4.1.2 — Prime implicants, essential prime implicants, minimal SOP and POS
Q7 Answer: (C)1 mark
Its cells are all covered by the four essential terms.
- (A) is wrong: No.
- (B) is wrong: It can't be enlarged.
- (D) is wrong: Every cell has another cover.
Re-read: Lesson 4.1.2 — Prime implicants, essential prime implicants, minimal SOP and POS
Q8 Answer: (B)2 marks
Group the 0s 0, 1 and 4, 6, 12, 14.
- (A) is wrong: Not this function.
- (C) is wrong: (A + C) is also 0 at 4 and 5, but 5 is a 1.
- (D) is wrong: Complemented literals in the wrong places.
Re-read: Lesson 4.1.2 — Prime implicants, essential prime implicants, minimal SOP and POS
Q9 Answer: 62 marks
Three 2-literal terms.
Re-read: Lesson 4.1.2 — Prime implicants, essential prime implicants, minimal SOP and POS
Q10 Answer: 22 marks
A + B.
Re-read: Lesson 4.1.3 — Don't-care conditions and 5-variable maps
Q11 Answer: (A)1 mark
Optional 1.
- (B) is wrong: No.
- (C) is wrong: Only real 1s decide.
- (D) is wrong: No.
Re-read: Lesson 4.1.3 — Don't-care conditions and 5-variable maps
Q12 Answer: 42 marks
2⁵⁻³.
Re-read: Lesson 4.1.3 — Don't-care conditions and 5-variable maps
Q13 Answer: (B)1 mark
Unticked terms cannot be merged further.
- (A) is wrong: Earlier columns can contain PIs too.
- (C) is wrong: No.
- (D) is wrong: Those were usually merged.
Re-read: Lesson 4.2.1 — The Quine–McCluskey tabular method
Q14 Answer: 21 mark
1--0.
Re-read: Lesson 4.2.1 — The Quine–McCluskey tabular method
Q15 Answer: (C)1 mark
They help form larger terms but need not be covered.
- (A) is wrong: They are used in merging.
- (B) is wrong: No.
- (D) is wrong: Reversed.
Re-read: Lesson 4.2.1 — The Quine–McCluskey tabular method