GATE CS 2016 Set 2 — Question 19
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Digital Logic → Number Systems & Arithmetic → Signed Number Representations
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Question
Let be the number of distinct 16-bit integers in 2’s complement representation. Let be the number of distinct 16-bit integers in sign magnitude representation.
Then is _______.
Then is _______.
Correct answer
1 to 1
Solution
For an -bit integer representation:
1.2's Complement Representation:
- Range of values:
- For , the range is .
- The number of distinct values is .
- So, .
- Range of values:
- For , the range is .
- Note that in sign magnitude, there are two representations for zero ( and ), which correspond to the same integer value . Therefore, the number of distinct integer values is .
- So, .
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