Vaidikalaya

MCQ On Complements 1s, 2s, 9s,10s

Q1. The 1’s complement of binary number 101011 is.
  1. 010100
  2. 010101
  3. 110100
  4. 101100

Answer: a, 010100

Solution:

1’s complement = invert all bits (1->0, 0->1)
101011 -> 010100

Q2. The 2’s complement of binary number 101011 is.
  1. 010101
  2. 010100
  3. 010101 + 1
  4. 010101

Answer: d, 010101

Solution:

1's complement = 010100
Add 1 -> 010100+1 = 010101

Q3. The 2’s complement of 0000 in a 4-bit system is.
  1. 0000
  2. 1111
  3. 1000
  4. Not defined

Answer: a, 0000

Solution:

0000 -> 1's complement = 1111
2's = 1111+1 = 10000
For 4-bit system = 0000 (discard carry)

Q4. Which of the following represents ?5 in 2's complement (4-bit system)?.
  1. 0101
  2. 1011
  3. 1101
  4. 1001

Answer: b, 1011

Solution:

+5 = 0101
1's complement -> 1010 
2's complement -> 1010 +1 = 1011 (-5)

Q5. Which statement is TRUE about 1’s and 2’s complement?.
  1. 1’s complement has only one zero
  2. 2’s complement has two zeros
  3. 1’s complement has two zeros
  4. 2’s complement has two representations of zero

Answer: c, 1’s complement has two zeros

Solution:

1's complement has +0 (0000) and ?0 (1111)
2's complement has only one zero

Q6. The 7's and 8's complement of octal number 356 is.
  1. 421, 422
  2. 401, 402
  3. 432, 444
  4. 311, 434

Answer: a, 421, 422

Solution:

7's complement = subtract each digit from 7
777-356 = 421
8's complement = 7's complement + 1 = 421 + 1 = 422

Q7. The 8's complement of 000 in octal is.
  1. 000
  2. 777
  3. 1000
  4. Not possible

Answer: a, 000

Solution:

8's complement = 7's complement + 1
7's complement of 000 = 777
8's complement = 777+1 = 1000
Since we are working with the same number of digits (3 digits), the extra carry is discarded.
Final result = 000

Q8. The 9's and 10's complement of decimal number 385 is.
  1. 614, 615
  2. 624, 616
  3. 615, 614
  4. 514, 617

Answer: a, 614, 615

Solution:

9's complement = subtract each digit from 9
999-385 = 614
10’s complement = 9’s complement + 1
614 + 1 = 615

Q9. If the 9’s complement of a number is 246, the number is.
  1. 753
  2. 654
  3. 764
  4. 864

Answer: a, 753

Solution:

Original digit = 9 ? complement = 9-246 = 753

Q10. Which complement is used for subtraction in binary systems?.
  1. 1’s complement
  2. 2’s complement
  3. 7’s complement
  4. 9’s complement

Answer: b, 2’s complement

Solution: Binary subtraction is efficiently performed using 2’s complement.

Q11. General rule: r's complement is obtained by.
  1. (r-1)'s complement + 1
  2. r's complement - 1
  3. r's complement + 1
  4. r - number

Answer: a, (r-1)'s complement + 1

Solution:

r's complement = (r-1)'s complement + 1

  • 2's = 1's + 1
  • 8's = 7's + 1
  • 10's = 9's + 1

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