The last practice set. Time yourself: 1-mark questions under 90 seconds, 2-mark under 3 minutes.
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12 questions · 18 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 markBits
Minimum number of bits for the unsigned number 5000?
Numerical answer: ________
Q2NAT2 marksArithmetic shift
−100 in 8-bit 2's complement is arithmetic-shifted right by 2. What value results?
Numerical answer: ________
Q3MCQ1 markExcess-3
The excess-3 code of the decimal number 42 is:
- (A) 0111 0101
- (B) 0111 0100
- (C) 0101 0111
- (D) 0100 0010
Q4NAT2 marksGap
In single precision, the gap between consecutive floats in [64, 128) is 2ᵏ. What is k?
Numerical answer: ________
Q5MCQ1 markGates
Which gate outputs 1 when an odd number of its inputs are 1?
- (A) NAND
- (B) XOR
- (C) OR
- (D) XNOR
Q6MSQ2 marksCompleteness
Which sets are functionally complete (no constants available)?
- (A) {AND, XNOR}
- (B) {NAND}
- (C) {XOR, NOT}
- (D) {OR, NOT}
Q7NAT2 marksPOS
F(A, B, C, D) = Σm(0, 2, 3, 4, 6, 7, 9, 11, 13, 15). How many literals are in its minimal POS?
Numerical answer: ________
Q8MCQ1 markFive variables
In a 5-variable K-map drawn as two halves (A = 0 and A = 1), a group of 8 cells uses 4 cells in each half at the same positions. How many literals does its term have?
- (A) 1
- (B) 3
- (C) 2
- (D) 4
Q9MCQ1 markDecoder
A 4-to-16 decoder with inputs A B C D: which output is 1 for ABCD = 1001?
- (A) Y₉
- (B) Y₁₀
- (C) Y₁
- (D) Y₆
Q10NAT2 marksROM
A ROM implements a 4-bit + 4-bit unsigned adder (no carry-in). How many bits does it store?
Numerical answer: ________
Q11NAT2 marksJK
A JK flip-flop starts at Q = 1. Edges with (J, K) = (0, 1), (1, 1), (1, 0), (1, 1). Final Q?
Numerical answer: ________
Q12NAT1 markDetector
Minimum number of states of a Mealy machine detecting the sequence 0110?
Numerical answer: ________
✓Answer Vault
Answer Vault
Try the questions first. Open when you are ready to check.
Q1 Answer: 131 mark
4096 ≤ 5000 < 8192.
Re-read: Lesson 0.1.1 — What "digital" means: bits, binary numbers and place value
Q2 Answer: -252 marks
−100 ÷ 4.
Re-read: Lesson 1.1.3 — Shifts, multiplication and Booth's algorithm
Q3 Answer: (A)1 mark
4 + 3 = 7, 2 + 3 = 5.
- (B) is wrong: Second digit wrong.
- (C) is wrong: Reversed.
- (D) is wrong: BCD.
Re-read: Lesson 1.2.1 — Binary codes: BCD, excess-3, Gray code and parity
Q4 Answer: -172 marks
6 − 23.
Re-read: Lesson 2.1.3 — IEEE 754 special values, denormals, range, precision and gaps
Q5 Answer: (B)1 mark
Parity.
- (A) is wrong: Not all.
- (C) is wrong: Any.
- (D) is wrong: Even number.
Re-read: Lesson 3.1.1 — Logic gates and truth tables
Q6 Answer: (B) (D)2 marks
NAND is universal; OR with NOT gives AND.
- (A) is wrong: Both preserve 1.
- (C) is wrong: Both linear.
Re-read: Lesson 3.2.2 — NAND and NOR as universal gates; functionally complete sets
Q7 Answer: 52 marks
(A' + D)(A + C + D'): two clauses.
Re-read: Lesson 4.1.2 — Prime implicants, essential prime implicants, minimal SOP and POS
Q8 Answer: (C)1 mark
8 = 2³ cells drop 3 of the 5 variables (A among them).
- (A) is wrong: That is a group of 16.
- (B) is wrong: That is a group of 4.
- (D) is wrong: That is a group of 2.
Re-read: Lesson 4.1.3 — Don't-care conditions and 5-variable maps
Q9 Answer: (A)1 mark
1001 = 9.
- (B) is wrong: 1010.
- (C) is wrong: 0001.
- (D) is wrong: Reversed bits.
Re-read: Lesson 5.2.2 — Decoders, encoders, priority encoders and demultiplexers
Q10 Answer: 12802 marks
8 inputs → 256 words of 5 bits.
Re-read: Lesson 5.2.3 — ROMs and PLAs: programmable logic
Q11 Answer: 02 marks
0, 1, 1, 0.
Re-read: Lesson 6.1.2 — Flip-flops: SR, D, JK and T; characteristic and excitation tables
Q12 Answer: 41 mark
k states for a k-bit sequence.
Re-read: Lesson 6.2.4 — Finite state machines: Mealy and Moore, sequence detectors, state minimisation