Phase 1 Checkpoint: 15 questions on signed numbers, binary arithmetic and codes.
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15 questions · 20 marks · 45 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 mark1's complement
−23 in 8-bit 1's complement is:
- (A) 1110 1000
- (B) 0001 0111
- (C) 1001 0111
- (D) 1110 1001
Q2NAT1 markRange
How many different values can a 5-bit 2's-complement number represent?
Numerical answer: ________
Q3NAT2 marksValue
The 8-bit pattern 1110 0111 is read as 2's complement. What value is it?
Numerical answer: ________
Q4MCQ1 markAsymmetry
In 8-bit 2's complement, the negative of −128 computed by "invert and add 1" is:
- (A) 0
- (B) +128
- (C) −127
- (D) −128
Q5NAT2 marksOverflow
In 8-bit 2's complement, 0111 0000 + 0011 0000 is computed. What value does the result pattern represent?
Numerical answer: ________
Q6MCQ2 marksCarries
For 1000 0001 + 1111 1111 (8-bit 2's complement), which is true?
- (A) Carry out 0 and overflow
- (B) Carry out 0 and no overflow
- (C) Carry out 1 and no overflow
- (D) Carry out 1 and overflow
Q7NAT1 markSign extension
The 6-bit 2's-complement number 101101 is sign-extended to 8 bits. What value does it represent?
Numerical answer: ________
Q8MCQ1 markMixed signs
Adding a positive and a negative 2's-complement number of the same width:
- (A) always overflows
- (B) never overflows
- (C) overflows if the result is negative
- (D) overflows if there is a carry out
Q9NAT1 markArithmetic shift
The 8-bit 2's-complement number 1110 0000 (−32) is arithmetic-shifted right by 2. What value results?
Numerical answer: ________
Q10NAT2 marksBooth
Booth's algorithm with the 8-bit multiplier 0011 1100: total additions plus subtractions?
Numerical answer: ________
Q11MCQ1 markBooth rule
In Booth's algorithm, the bit pair (Q₀, Q₋₁) = (0, 1) means:
- (A) add the multiplicand
- (B) shift only
- (C) subtract the multiplicand
- (D) stop
Q12NAT1 markBCD
How many bits does the BCD form of a 6-digit decimal number use?
Numerical answer: ________
Q13MCQ1 markBCD addition
In BCD addition, the digit sum 9 + 9 = 1 0010. What must be done?
- (A) Add 0110 because a carry was produced
- (B) Subtract 0110
- (C) Add 0011
- (D) Nothing; it is valid
Q14NAT2 marksGray
How many bits differ between the 4-bit Gray codes of 7 and 8?
Numerical answer: ________
Q15NAT1 markParity
An odd-parity bit is added to the data 1100 1010. What is the parity bit?
Numerical answer: ________
✓Answer Vault
Answer Vault
Try the questions first. Open when you are ready to check.
Q1 Answer: (A)1 mark
Invert 0001 0111.
- (B) is wrong: +23.
- (C) is wrong: Sign-magnitude.
- (D) is wrong: 2's complement.
Re-read: Lesson 1.1.1 — Sign-magnitude, 1's complement and 2's complement
Q2 Answer: 321 mark
2⁵ patterns, one zero.
Re-read: Lesson 1.1.1 — Sign-magnitude, 1's complement and 2's complement
Q3 Answer: -252 marks
−128 + 103.
Re-read: Lesson 1.1.1 — Sign-magnitude, 1's complement and 2's complement
Q4 Answer: (D)1 mark
1000 0000 → 0111 1111 + 1 = 1000 0000.
- (A) is wrong: No.
- (B) is wrong: Not representable.
- (C) is wrong: No.
Re-read: Lesson 1.1.1 — Sign-magnitude, 1's complement and 2's complement
Q5 Answer: -962 marks
112 + 48 = 160 wraps to 160 − 256.
Re-read: Lesson 1.1.2 — 2's-complement arithmetic: addition, subtraction, overflow, sign extension
Q6 Answer: (C)2 marks
−127 + −1 = −128 fits; carries into and out of the MSB are both 1.
- (A) is wrong: Carry out is 1.
- (B) is wrong: Carry out is 1.
- (D) is wrong: No overflow.
Re-read: Lesson 1.1.2 — 2's-complement arithmetic: addition, subtraction, overflow, sign extension
Q7 Answer: -191 mark
−32 + 13.
Re-read: Lesson 1.1.2 — 2's-complement arithmetic: addition, subtraction, overflow, sign extension
Q8 Answer: (B)1 mark
The result lies between the two operands.
- (A) is wrong: No.
- (C) is wrong: No.
- (D) is wrong: Carry out is not overflow.
Re-read: Lesson 1.1.2 — 2's-complement arithmetic: addition, subtraction, overflow, sign extension
Q9 Answer: -81 mark
1111 1000.
Re-read: Lesson 1.1.3 — Shifts, multiplication and Booth's algorithm
Q10 Answer: 22 marks
One run of 1s: subtract at its start, add after its end.
Re-read: Lesson 1.1.3 — Shifts, multiplication and Booth's algorithm
Q11 Answer: (A)1 mark
A run of 1s has just ended.
- (B) is wrong: That is 00 or 11.
- (C) is wrong: That is (1, 0).
- (D) is wrong: No.
Re-read: Lesson 1.1.3 — Shifts, multiplication and Booth's algorithm
Q12 Answer: 241 mark
4 per digit.
Re-read: Lesson 1.2.1 — Binary codes: BCD, excess-3, Gray code and parity
Q13 Answer: (A)1 mark
Carry out of the digit means the sum exceeded 9.
- (B) is wrong: No.
- (C) is wrong: That is excess-3.
- (D) is wrong: 0010 alone would be wrong.
Re-read: Lesson 1.2.1 — Binary codes: BCD, excess-3, Gray code and parity
Q14 Answer: 12 marks
Consecutive Gray codes differ in one bit (0100 and 1100).
Re-read: Lesson 1.2.1 — Binary codes: BCD, excess-3, Gray code and parity
Q15 Answer: 11 mark
Four 1s; odd parity needs one more.
Re-read: Lesson 1.2.1 — Binary codes: BCD, excess-3, Gray code and parity