GATE CS 2016 Set 1 — Question 17
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Digital Logic → Number Systems & Arithmetic → Signed Number Representations
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Question
The 16-bit 2’s complement representation of an integer is 1111 1111 1111 0101; its decimal representation is ________.
Correct answer
-11
Solution
The given 16-bit number is . Since the Most Significant Bit (MSB) is 1, it is a negative number in 2's complement representation.To find its magnitude, we take the 2's complement of the number:
Thus, the decimal representation is .
1.Invert all bits:
2.Add 1:
The magnitude is .Thus, the decimal representation is .
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