Let \(X\) be the number of distinct 16-bit integers in 2’s complement…
2016
Let \(X\) be the number of distinct 16-bit integers in 2’s complement representation. Let \(Y\) be the number of distinct 16-bit integers in sign magnitude representation.
Then \(X −Y\) is ____________ .
Attempted by 260 students.
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Correct answer: 1
Answer: 1
Explanation:
Number of distinct 16-bit integers in two's complement (X): Every 16-bit bit pattern maps to a unique integer, so X = 2^16 = 65536.
Number of distinct 16-bit integers in sign-magnitude (Y): There are 2^16 bit patterns, but +0 and -0 represent the same integer, so Y = 2^16 − 1 = 65535.
Therefore X − Y = 65536 − 65535 = 1.
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