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Stop here until you have finished the 90-minute final test.
Answer Vault
Try the questions first. Open when you are ready to check.
Q1 Answer: 111 mark
1024 ≤ 2000 < 2048.
Re-read: Lesson 0.1.1 — What "digital" means: bits, binary numbers and place value
Q2 Answer: 801 mark
63 + 17.
Re-read: Lesson 0.1.2 — Octal, hexadecimal and converting between any two bases
Q3 Answer: -561 mark
−128 + 64 + 8.
Re-read: Lesson 1.1.1 — Sign-magnitude, 1's complement and 2's complement
Q4 Answer: (B)1 mark
V = C_in ⊕ C_out at the MSB.
- (A) is wrong: Different signs never overflow.
- (C) is wrong: No.
- (D) is wrong: Not for signed numbers.
Re-read: Lesson 1.1.2 — 2's-complement arithmetic: addition, subtraction, overflow, sign extension
Q5 Answer: (A)1 mark
9 → 1001, 3 → 0011.
- (B) is wrong: Second digit wrong.
- (C) is wrong: Excess-3.
- (D) is wrong: Binary 93.
Re-read: Lesson 1.2.1 — Binary codes: BCD, excess-3, Gray code and parity
Q6 Answer: 1281 mark
1.0 × 2¹.
Re-read: Lesson 2.1.2 — Floating point and IEEE 754: sign, biased exponent, mantissa
Q7 Answer: (D)1 mark
0.F × 2⁻¹²⁶.
- (A) is wrong: Needs F = 0.
- (B) is wrong: Needs E = 255.
- (C) is wrong: Needs E = 255.
Re-read: Lesson 2.1.3 — IEEE 754 special values, denormals, range, precision and gaps
Q8 Answer: (B)1 mark
NOT of AND.
- (A) is wrong: 1 only when both are 1.
- (C) is wrong: 0 unless both are 0.
- (D) is wrong: 0 when inputs differ.
Re-read: Lesson 3.1.1 — Logic gates and truth tables
Q9 Answer: (C)1 mark
Redundant literal rule.
- (A) is wrong: Misses row 01.
- (B) is wrong: No.
- (D) is wrong: Misses row 10.
Re-read: Lesson 3.1.2 — Boolean algebra: laws, duality, De Morgan and algebraic simplification
Q10 Answer: 81 mark
2⁵⁻².
Re-read: Lesson 3.2.1 — Canonical forms: minterms, maxterms, SOP and POS
Q11 Answer: 31 mark
Two NOTs and a NOR.
Re-read: Lesson 3.2.2 — NAND and NOR as universal gates; functionally complete sets
Q12 Answer: (A)1 mark
The four corners.
- (B) is wrong: A diagonal.
- (C) is wrong: Not a rectangle.
- (D) is wrong: 1, 2 are not adjacent.
Re-read: Lesson 4.1.1 — Karnaugh maps for 2, 3 and 4 variables: adjacency and grouping
Q13 Answer: (D)1 mark
Dashes aligned; one other bit differs.
- (A) is wrong: Four bits differ.
- (B) is wrong: Dashes in different places.
- (C) is wrong: Dashes in different places.
Re-read: Lesson 4.2.1 — The Quine–McCluskey tabular method
Q14 Answer: 11 mark
Exactly one minterm.
Re-read: Lesson 5.2.2 — Decoders, encoders, priority encoders and demultiplexers
Q15 Answer: 121 mark
2n.
Re-read: Lesson 6.2.1 — Registers, shift registers, ring and Johnson counters
Q16 Answer: 72 marks
2b² + 3b + 5 = 124.
Re-read: Lesson 0.1.2 — Octal, hexadecimal and converting between any two bases
Q17 Answer: 32 marks
Digits 0 −1 0 +1 0 −1 0 0.
Re-read: Lesson 1.1.3 — Shifts, multiplication and Booth's algorithm
Q18 Answer: 20.52 marks
E = 131 → e = 4; 1.01001₂ × 2⁴ = 10100.1₂.
Re-read: Lesson 2.1.2 — Floating point and IEEE 754: sign, biased exponent, mantissa
Q19 Answer: 15.52 marks
E = 110 → e = 3; 1.1111₂ × 2³.
Re-read: Lesson 2.1.3 — IEEE 754 special values, denormals, range, precision and gaps
Q20 Answer: (B)2 marks
Dual of the consensus theorem: the clause (B + C) is redundant. Both sides equal A'B + AC.
- (A) is wrong: Row 001 gives 1, but the original is 0 (A + B = 0).
- (C) is wrong: That equals B + AC, which is 1 at row 110 where the original is 0.
- (D) is wrong: Also 1 at row 110 (A' + C = 0 there, so the original is 0).
Re-read: Lesson 3.1.2 — Boolean algebra: laws, duality, De Morgan and algebraic simplification
Q21 Answer: 163842 marks
2¹⁴: the other 14 rows are free.
Re-read: Lesson 3.2.3 — Counting Boolean functions; self-dual functions; XOR tricks
Q22 Answer: 122 marks
Four essential 3-literal terms; the centre BD is not needed.
Re-read: Lesson 4.1.2 — Prime implicants, essential prime implicants, minimal SOP and POS
Q23 Answer: 12 marks
Only B'C' is essential.
Re-read: Lesson 4.1.2 — Prime implicants, essential prime implicants, minimal SOP and POS
Q24 Answer: 82 marks
For example B'D' + A'BC + AC'D.
Re-read: Lesson 4.1.3 — Don't-care conditions and 5-variable maps
Q25 Answer: 652 marks
31 × 2 + 3.
Re-read: Lesson 5.1.2 — Half adder, full adder and the ripple-carry adder
Q26 Answer: (C)2 marks
A = 0 passes B ⊕ C, A = 1 inverts it.
- (A) is wrong: No.
- (B) is wrong: Inverted.
- (D) is wrong: Ignores A.
Re-read: Lesson 5.2.1 — Multiplexers, and implementing functions with them
Q27 Answer: 402 marks
Period 25 ns.
Re-read: Lesson 6.1.3 — Converting flip-flops; timing and the maximum clock frequency
Q28 Answer: 62.52 marks
4 MHz / 64.
Re-read: Lesson 6.2.2 — Asynchronous (ripple) counters and mod-N counters
Q29 Answer: (B)2 marks
00 → 01 (Q₀ set) → 11 (Q₁ toggles) → 00 (both reset/toggle).
- (A) is wrong: No.
- (C) is wrong: That is a binary counter.
- (D) is wrong: No.
Re-read: Lesson 6.2.3 — Synchronous counters: analysis and design
Q30 Answer: 42 marks
Matches end at positions 3, 6, 8 and 10.
Re-read: Lesson 6.2.4 — Finite state machines: Mealy and Moore, sequence detectors, state minimisation