Phase 0 Checkpoint: 15 questions on number systems and binary arithmetic.
⏱️
15 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.
Q1NAT1 markBinary
What is 11111111₂ in decimal?
Numerical answer: ________
Q2MCQ1 markDecimal to binary
What is 37 in binary?
- (A) 100011
- (B) 100101
- (C) 110001
- (D) 101001
Q3NAT1 markBits
Minimum number of bits to represent 99?
Numerical answer: ________
Q4NAT1 markHex
What is 5D₁₆ in decimal?
Numerical answer: ________
Q5MCQ1 markBinary to octal
1101101₂ in octal is:
- (A) 665
- (B) 551
- (C) 155
- (D) 135
Q6NAT2 marksFraction
What is 7.4₈ in decimal (1 decimal place)?
Numerical answer: ________
Q7MCQ2 marksFraction
What is 25.25 in binary?
- (A) 11001.01
- (B) 11010.01
- (C) 11001.1
- (D) 10011.01
Q8MCQ2 marksFind the base
For which base b is 33_b × 3 = 132_b? (Hint: write both sides as polynomials in b.)
- (A) 5
- (B) 7
- (C) 4
- (D) 6
Q9NAT1 markHex addition
What is 9F₁₆ + 2C₁₆, in decimal?
Numerical answer: ________
Q10MCQ1 markNon-terminating
Which of these decimal fractions does NOT end in binary?
- (A) 0.75
- (B) 0.125
- (C) 0.1
- (D) 0.5
Q11NAT1 markAddition
What is 1111₂ + 0001₂, in decimal?
Numerical answer: ________
Q12NAT1 markSubtraction
What is 10000₂ − 00001₂, in decimal?
Numerical answer: ________
Q13MCQ1 markShift
Shifting an unsigned number right by 3 places:
- (A) multiplies it by 8
- (B) does not change it
- (C) divides it by 3
- (D) divides it by 8, dropping the remainder
Q14NAT2 marksCarry out
In an 8-bit unsigned adder, 200 + 100 is computed. What value is left in the 8 result bits?
Numerical answer: ________
Q15NAT2 marksProduct size
Minimum number of bits needed for the product of a 10-bit and a 7-bit unsigned number?
Numerical answer: ________
✓Answer Vault
Answer Vault
Try the questions first. Open when you are ready to check.
Q1 Answer: 2551 mark
2⁸ − 1.
Re-read: Lesson 0.1.1 — What "digital" means: bits, binary numbers and place value
Q2 Answer: (B)1 mark
32 + 4 + 1.
- (A) is wrong: That is 35.
- (C) is wrong: That is 49.
- (D) is wrong: That is 41.
Re-read: Lesson 0.1.1 — What "digital" means: bits, binary numbers and place value
Q3 Answer: 71 mark
64 ≤ 99 < 128.
Re-read: Lesson 0.1.1 — What "digital" means: bits, binary numbers and place value
Q4 Answer: 931 mark
5 × 16 + 13.
Re-read: Lesson 0.1.2 — Octal, hexadecimal and converting between any two bases
Q5 Answer: (C)1 mark
001 101 101.
- (A) is wrong: Grouped from the wrong end.
- (B) is wrong: Reversed.
- (D) is wrong: That is 1011101₂.
Re-read: Lesson 0.1.2 — Octal, hexadecimal and converting between any two bases
Q6 Answer: 7.52 marks
7 + 4/8.
Re-read: Lesson 0.1.2 — Octal, hexadecimal and converting between any two bases
Q7 Answer: (A)2 marks
25 = 16 + 8 + 1; 0.25 = 0.01₂.
- (B) is wrong: That is 26.25.
- (C) is wrong: That is 25.5.
- (D) is wrong: That is 19.25.
Re-read: Lesson 0.1.2 — Octal, hexadecimal and converting between any two bases
Q8 Answer: (B)2 marks
9b + 9 = b² + 3b + 2, so b² − 6b − 7 = 0, i.e. (b − 7)(b + 1) = 0.
- (A) is wrong: 33₅ × 3 = 54, but 132₅ = 42.
- (C) is wrong: 33₄ × 3 = 45, but 132₄ = 30.
- (D) is wrong: 33₆ × 3 = 63, but 132₆ = 56.
Re-read: Lesson 0.1.2 — Octal, hexadecimal and converting between any two bases
Q9 Answer: 2031 mark
159 + 44.
Re-read: Lesson 0.1.2 — Octal, hexadecimal and converting between any two bases
Q10 Answer: (C)1 mark
1/10 has the prime factor 5.
- (A) is wrong: 3/4.
- (B) is wrong: 1/8.
- (D) is wrong: 1/2.
Re-read: Lesson 0.1.2 — Octal, hexadecimal and converting between any two bases
Q11 Answer: 161 mark
15 + 1.
Re-read: Lesson 0.1.3 — Binary arithmetic by hand; how many values n bits can hold
Q12 Answer: 151 mark
16 − 1.
Re-read: Lesson 0.1.3 — Binary arithmetic by hand; how many values n bits can hold
Q13 Answer: (D)1 mark
Each right shift halves.
- (A) is wrong: That is a left shift.
- (B) is wrong: It changes.
- (C) is wrong: Powers of 2, not 3.
Re-read: Lesson 0.1.3 — Binary arithmetic by hand; how many values n bits can hold
Q14 Answer: 442 marks
300 − 256.
Re-read: Lesson 0.1.3 — Binary arithmetic by hand; how many values n bits can hold
Q15 Answer: 172 marks
10 + 7.
Re-read: Lesson 0.1.3 — Binary arithmetic by hand; how many values n bits can hold