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The number of 1’s in the 8-bit unsigned representation of 127 in its 2’s complement form is m and that in 1’s complement form is n. What is the value of m : n?
  • a)
    2 : 1
  • b)
    1 : 2
  • c)
    3 : 1
  • d)
    1 : 3
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
The number of 1’s in the 8-bit unsigned representation of 127 in...
Understanding the Problem:
In 2's complement form, the most significant bit represents the sign of the number, while in 1's complement form, the most significant bit is used for both sign and magnitude representation.

Calculating 2's Complement of 127:
- 127 in binary is 01111111
- To find the 2's complement, we invert all the bits and add 1
- Inverting all the bits: 10000000
- Adding 1: 10000001
- Number of 1's in the 2's complement form of 127 (10000001) is 2

Calculating 1's Complement of 127:
- In 1's complement form, we only invert the bits
- Inverting all the bits of 127 (01111111): 10000000
- Number of 1's in the 1's complement form of 127 (10000000) is 1

Calculating Ratio:
- Number of 1's in 2's complement form (m) = 2
- Number of 1's in 1's complement form (n) = 1
- Therefore, the ratio of m:n = 2:1
Therefore, the correct answer is option A) 2:1.
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Community Answer
The number of 1’s in the 8-bit unsigned representation of 127 in...
Concept:
1’s complement representation of a binary number is obtained by toggling all the bits, i.e. replacing 1 with 0, and 0 with 1.
2’s complement representation of a binary number is obtained by adding 1 to the 1’s complement representation.
Application:
(127)10 = (01111111)2
1’s complement representation will be:
1’s complement = 10000000
Number of 1’s is the 1’s complement is, n = 1
Now, the two (2’s) complement representation will be:
2’s complement = 10000000 + 1
= 10000001
Number of 1’s in 2’s complement is, m = 2
∴ The required ratio is m : n = 2 : 1
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The number of 1’s in the 8-bit unsigned representation of 127 in its 2’s complement form is m and that in 1’s complement form is n. What is the value of m : n?a)2 : 1b)1 : 2c)3 : 1d)1 : 3Correct answer is option 'A'. Can you explain this answer?
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