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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...
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.
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
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...
The number of 1 can refer to different things depending on the context. It could refer to:
- The quantity of the digit 1: In this case, the number of 1 would simply mean the count or total number of occurrences of the digit 1.
- The value of 1: This could refer to a specific number or quantity represented by the digit 1. For example, if we're talking about a specific number like 111, then the number of 1 would be 3.
- A placeholder or position in a number system: In a positional number system like decimal or binary, the number of 1 in a specific position represents its value. For example, in the decimal number 123, the number of 1 in the hundreds place is 1.
Without further information or context, it is not possible to determine the specific meaning of "the number of 1."
- The quantity of the digit 1: In this case, the number of 1 would simply mean the count or total number of occurrences of the digit 1.
- The value of 1: This could refer to a specific number or quantity represented by the digit 1. For example, if we're talking about a specific number like 111, then the number of 1 would be 3.
- A placeholder or position in a number system: In a positional number system like decimal or binary, the number of 1 in a specific position represents its value. For example, in the decimal number 123, the number of 1 in the hundreds place is 1.
Without further information or context, it is not possible to determine the specific meaning of "the number of 1."
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