Phase 3 Checkpoint: 15 questions on gates, Boolean algebra, canonical forms and completeness.
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15 questions · 21 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 markGates
The output of a 2-input XNOR gate is 1 when:
- (A) the inputs are equal
- (B) the inputs differ
- (C) both inputs are 1 only
- (D) at least one input is 1
Q2NAT1 markTruth table
F(A, B, C) = (A + B)C'. In how many rows is F = 1?
Numerical answer: ________
Q3MCQ1 markLaw
Which equality is FALSE?
- (A) A + 1 = 1
- (B) A + A' = 0
- (C) A + A = A
- (D) A · A' = 0
Q4MCQ2 marksSimplify
AB + A'C + BC + AB'C simplifies to:
- (A) A + C
- (B) C
- (C) AB + A'C
- (D) AB + C
Q5MCQ1 markDual
The dual of (A + B')C is:
- (A) A'B + C'
- (B) (A' + B)C'
- (C) AB' + C
- (D) A + B'C
Q6NAT1 markMinterm number
For F(A, B, C, D), which minterm number is AB'CD?
Numerical answer: ________
Q7NAT2 marksCanonical
F(A, B, C) = AB + B'C. How many maxterms does its canonical POS have?
Numerical answer: ________
Q8MCQ1 markPOS
A function is written as ΠM(0, 2). For which input does it output 0?
- (A) A B C = 0 0 1
- (B) A B C = 0 1 0
- (C) A B C = 1 0 0
- (D) A B C = 1 1 1
Q9NAT2 marksNAND count
F = AB + CD + EF is built as a two-level NAND–NAND circuit. How many NAND gates?
Numerical answer: ________
Q10NAT1 markNOR count
Minimum number of 2-input NOR gates for a 2-input XNOR?
Numerical answer: ________
Q11MSQ2 marksCompleteness
Which sets are functionally complete? (Constants are NOT available.)
- (A) {AND, NOT}
- (B) {NAND}
- (C) {implication}
- (D) {XOR, AND}
Q12MCQ1 markTwo-level
A POS expression is realised directly by:
- (A) NAND–NAND
- (B) XOR–XOR
- (C) NOR–NOR
- (D) AND–OR
Q13NAT1 markCounting
How many Boolean functions of 3 variables are there?
Numerical answer: ________
Q14NAT2 marksCounting
How many functions of 4 variables have exactly 2 minterms?
Numerical answer: ________
Q15NAT2 marksSelf-dual
How many self-dual functions of 2 variables are there?
Numerical answer: ________
✓Answer Vault
Answer Vault
Try the questions first. Open when you are ready to check.
Q1 Answer: (A)1 mark
XNOR = NOT XOR.
- (B) is wrong: That is XOR.
- (C) is wrong: Too narrow.
- (D) is wrong: That is OR.
Re-read: Lesson 3.1.1 — Logic gates and truth tables
Q2 Answer: 31 mark
C = 0 and A + B = 1: rows 2, 4, 6.
Re-read: Lesson 3.1.1 — Logic gates and truth tables
Q3 Answer: (B)1 mark
A + A' = 1.
- (A) is wrong: Null law.
- (C) is wrong: Idempotent.
- (D) is wrong: Complement law.
Re-read: Lesson 3.1.2 — Boolean algebra: laws, duality, De Morgan and algebraic simplification
Q4 Answer: (D)2 marks
Minterms: AB gives 6, 7; A'C gives 1, 3; BC gives 3, 7; AB'C gives 5. Together {1, 3, 5, 6, 7}: every row with C = 1, plus row 6 (110), which is AB + C.
- (A) is wrong: Row 100 gives 0 in the original.
- (B) is wrong: Misses row 110.
- (C) is wrong: Misses row 101.
Re-read: Lesson 3.1.2 — Boolean algebra: laws, duality, De Morgan and algebraic simplification
Q5 Answer: (C)1 mark
Swap + and ·.
- (A) is wrong: Variables complemented.
- (B) is wrong: That is a complement attempt.
- (D) is wrong: Wrong grouping.
Re-read: Lesson 3.1.2 — Boolean algebra: laws, duality, De Morgan and algebraic simplification
Q6 Answer: 111 mark
Re-read: Lesson 3.2.1 — Canonical forms: minterms, maxterms, SOP and POS
Q7 Answer: 42 marks
Minterms 1, 5, 6, 7; the other four rows are maxterms.
Re-read: Lesson 3.2.1 — Canonical forms: minterms, maxterms, SOP and POS
Q8 Answer: (B)1 mark
Row 2.
- (A) is wrong: Row 1.
- (C) is wrong: Row 4.
- (D) is wrong: Row 7.
Re-read: Lesson 3.2.1 — Canonical forms: minterms, maxterms, SOP and POS
Q9 Answer: 42 marks
Three first-level gates and one output gate.
Re-read: Lesson 3.2.2 — NAND and NOR as universal gates; functionally complete sets
Q10 Answer: 41 mark
The dual of the 4-NAND XOR.
Re-read: Lesson 3.2.2 — NAND and NOR as universal gates; functionally complete sets
Q11 Answer: (A) (B)2 marks
NAND is universal; AND with NOT covers everything.
- (C) is wrong: Implication preserves 1.
- (D) is wrong: Both preserve 0.
Re-read: Lesson 3.2.2 — NAND and NOR as universal gates; functionally complete sets
Q12 Answer: (C)1 mark
Replace ORs and the final AND by NORs.
- (A) is wrong: That suits SOP.
- (B) is wrong: No.
- (D) is wrong: That suits SOP with plain gates.
Re-read: Lesson 3.2.2 — NAND and NOR as universal gates; functionally complete sets
Q13 Answer: 2561 mark
2⁸.
Re-read: Lesson 3.2.3 — Counting Boolean functions; self-dual functions; XOR tricks
Q14 Answer: 1202 marks
C(16, 2).
Re-read: Lesson 3.2.3 — Counting Boolean functions; self-dual functions; XOR tricks
Q15 Answer: 42 marks
2^(2¹): A, B, A', B'.
Re-read: Lesson 3.2.3 — Counting Boolean functions; self-dual functions; XOR tricks