Twelve questions from all phases, mixed on purpose so you must first recognise which idea each needs. Conventions as in the front matter.
⏱️
12 questions · 19 marks · 40 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.
Q1NAT1 markBase conversion
What is A7₁₆ in decimal?
Numerical answer: ________
Q2MCQ1 mark2's complement
−45 in 8-bit 2's complement is:
- (A) 1101 0010
- (B) 1101 0011
- (C) 0010 1101
- (D) 1010 1101
Q3NAT2 marksOverflow
In 8-bit 2's complement, 0101 0000 + 0011 0000 is computed. What value does the 8-bit result represent?
Numerical answer: ________
Q4NAT1 markIEEE exponent
What is the exponent field (decimal) of 6.5 in IEEE 754 single precision?
Numerical answer: ________
Q5MCQ1 markSimplification
A'B + AB + AB' simplifies to:
- (A) B
- (B) AB
- (C) A ⊕ B
- (D) A + B
Q6NAT2 marksMinterms
F(A, B, C, D) = A'B + CD. How many minterms does F have?
Numerical answer: ________
Q7NAT2 marksNAND count
Minimum number of 2-input NAND gates for F = AB + C' (C' is not available, only A, B, C)?
Numerical answer: ________
Q8NAT2 marksK-map
F(A, B, C, D) = Σm(1, 3, 5, 7, 8, 10, 12, 14). How many literals are in the minimal SOP?
Numerical answer: ________
Q9NAT2 marksPrime implicants
F(A, B, C, D) = Σm(0, 2, 3, 4, 6, 7, 9, 11, 13, 15). How many prime implicants does it have?
Numerical answer: ________
Q10NAT2 marksRipple adder
A 10-bit ripple-carry adder has full-adder carry delay 3 ns and sum delay 5 ns. When is the most significant sum bit valid (ns)?
Numerical answer: ________
Q11MCQ2 marksMultiplexer
A 4:1 MUX has S₁ = A, S₀ = B and data inputs I₀ = 1, I₁ = C, I₂ = C', I₃ = 0. Its output is:
- (A) A'B'C' + ABC
- (B) A ⊕ B ⊕ C
- (C) A'C + B'C'
- (D) A'B' + BC
Q12NAT1 markCounter
Minimum number of flip-flops for a mod-24 counter?
Numerical answer: ________
✓Answer Vault
Answer Vault
Try the questions first. Open when you are ready to check.
Q1 Answer: 1671 mark
10 × 16 + 7.
Re-read: Lesson 0.1.2 — Octal, hexadecimal and converting between any two bases
Q2 Answer: (B)1 mark
Invert 0010 1101 and add 1.
- (A) is wrong: 1's complement.
- (C) is wrong: +45.
- (D) is wrong: Sign-magnitude.
Re-read: Lesson 1.1.1 — Sign-magnitude, 1's complement and 2's complement
Q3 Answer: -1282 marks
80 + 48 = 128 overflows to 1000 0000.
Re-read: Lesson 1.1.2 — 2's-complement arithmetic: addition, subtraction, overflow, sign extension
Q4 Answer: 1291 mark
1.101 × 2² → 2 + 127.
Re-read: Lesson 2.1.2 — Floating point and IEEE 754: sign, biased exponent, mantissa
Q5 Answer: (D)1 mark
A'B + AB = B; B + AB' = A + B.
- (A) is wrong: Misses row 10.
- (B) is wrong: Too small.
- (C) is wrong: Misses row 11.
Re-read: Lesson 3.1.2 — Boolean algebra: laws, duality, De Morgan and algebraic simplification
Q6 Answer: 72 marks
4 + 4 − 1 (A'BCD counted twice).
Re-read: Lesson 3.2.1 — Canonical forms: minterms, maxterms, SOP and POS
Q7 Answer: 22 marks
NAND(NAND(A, B), C) = AB + C'.
Re-read: Lesson 3.2.2 — NAND and NOR as universal gates; functionally complete sets
Q8 Answer: 42 marks
A'D + AD' (= A ⊕ D).
Re-read: Lesson 4.1.1 — Karnaugh maps for 2, 3 and 4 variables: adjacency and grouping
Q9 Answer: 42 marks
A'D', A'C, CD, AD.
Re-read: Lesson 4.1.2 — Prime implicants, essential prime implicants, minimal SOP and POS
Q10 Answer: 322 marks
9 × 3 + 5.
Re-read: Lesson 5.1.2 — Half adder, full adder and the ripple-carry adder
Q11 Answer: (C)2 marks
Minterms 0, 1, 3, 4.
- (A) is wrong: Only two minterms.
- (B) is wrong: Parity is 1, 2, 4, 7.
- (D) is wrong: Misses m₄ (100).
Re-read: Lesson 5.2.1 — Multiplexers, and implementing functions with them
Q12 Answer: 51 mark
16 < 24 ≤ 32.
Re-read: Lesson 6.2.2 — Asynchronous (ripple) counters and mod-N counters