Twelve more mixed questions. Before computing, name the lesson each one comes from.
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12 questions · 20 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.
Q1MCQ1 markOctal to hex
7456₈ in hexadecimal is:
- (A) F2E
- (B) 7456
- (C) 3CE
- (D) E2F
Q2NAT1 markRange
What is the largest value of a 10-bit 2's-complement number?
Numerical answer: ________
Q3NAT2 marksBooth
How many additions plus subtractions does Booth's algorithm perform for the multiplier 0110 1101?
Numerical answer: ________
Q4NAT1 markGray code
The Gray code 1101 is converted to binary. What decimal value results?
Numerical answer: ________
Q5NAT2 marksFixed point
Signed (2's-complement) fixed point with 3 integer bits (including the sign) and 5 fraction bits. Most negative value?
Numerical answer: ________
Q6NAT2 marksIEEE decode
What value does the single-precision pattern 0xC110 0000 represent?
Numerical answer: ________
Q7MCQ1 markDuality
The dual of A(B + C) = AB + AC is:
- (A) A(BC) = (AB)(AC)
- (B) A + B + C = AB + AC
- (C) A'(B' + C') = A'B' + A'C'
- (D) A + BC = (A + B)(A + C)
Q8NAT2 marksCounting
How many Boolean functions of 3 variables have exactly 2 minterms?
Numerical answer: ________
Q9NAT2 marksDon't-cares
F(A, B, C, D) = Σm(4, 8, 10, 11, 12, 15) + d(9, 14). How many literals are in its minimal SOP?
Numerical answer: ________
Q10NAT2 marksTabular method
F(A, B, C, D) = Σm(1, 4, 6, 7, 9, 12, 14, 15). How many prime implicants does the tabular method find?
Numerical answer: ________
Q11NAT2 marksLookahead
An 8-bit adder is two 4-bit carry-lookahead blocks connected in a ripple. P and G take 1 gate delay; a block's carry-out comes 2 gate delays after its carry-in. After how many gate delays is C₈ ready?
Numerical answer: ________
Q12NAT2 marksClock
t_pd = 3 ns, worst logic delay 9 ns, setup 2 ns, clock skew 1 ns. Maximum clock frequency in MHz (2 decimals)?
Numerical answer: ________
✓Answer Vault
Answer Vault
Try the questions first. Open when you are ready to check.
Q1 Answer: (A)1 mark
111 100 101 110 → 1111 0010 1110.
- (B) is wrong: Unchanged digits.
- (C) is wrong: Wrong grouping.
- (D) is wrong: Reversed.
Re-read: Lesson 0.1.2 — Octal, hexadecimal and converting between any two bases
Q2 Answer: 5111 mark
2⁹ − 1.
Re-read: Lesson 1.1.1 — Sign-magnitude, 1's complement and 2's complement
Q3 Answer: 62 marks
Digits +1 0 −1 +1 0 −1 +1 −1.
Re-read: Lesson 1.1.3 — Shifts, multiplication and Booth's algorithm
Q4 Answer: 91 mark
1, 1⊕1 = 0, 0⊕0 = 0, 0⊕1 = 1 → 1001.
Re-read: Lesson 1.2.1 — Binary codes: BCD, excess-3, Gray code and parity
Q5 Answer: -42 marks
−2².
Re-read: Lesson 2.1.1 — Fixed-point binary fractions: range, precision and rounding
Q6 Answer: -92 marks
S 1, E 130 → e = 3; 1.001₂ × 2³.
Re-read: Lesson 2.1.2 — Floating point and IEEE 754: sign, biased exponent, mantissa
Q7 Answer: (D)1 mark
Swap + and ·.
- (A) is wrong: Not a dual.
- (B) is wrong: Not a dual.
- (C) is wrong: Complements the variables.
Re-read: Lesson 3.1.2 — Boolean algebra: laws, duality, De Morgan and algebraic simplification
Q8 Answer: 282 marks
C(8, 2).
Re-read: Lesson 3.2.3 — Counting Boolean functions; self-dual functions; XOR tricks
Q9 Answer: 72 marks
AC + AB' + BC'D' (or AC + AD' + BC'D').
Re-read: Lesson 4.1.3 — Don't-care conditions and 5-variable maps
Q10 Answer: 32 marks
B'C'D, BD', BC.
Re-read: Lesson 4.2.1 — The Quine–McCluskey tabular method
Q11 Answer: 52 marks
3 for C₄, 5 for C₈.
Re-read: Lesson 5.1.3 — Carry-lookahead adder, adder–subtractor and comparators
Q12 Answer: 66.66 to 66.672 marks
Period 15 ns.
Re-read: Lesson 6.1.3 — Converting flip-flops; timing and the maximum clock frequency