The 16-bit 2's complement representation of an integer is 1111 1111 1111 0101; its decimal representation is …
Topic-wise GATE CS PYQs with verified steps
GATE CSE 2016 Set 1 · Q7
Time
Your answerNumerical answer
Solution
Official answer: -11 (±0)
Number Representation and ArithmeticThe given 16-bit binary number is:
Since the most significant bit (MSB) is , the number is negative in 2's complement representation.
To find its decimal value:
Find the 1's complement of the number:
Add to find the magnitude (2's complement of the negative number):
Apply the negative sign:
Alternatively, calculate the weighted sum directly:
Try the question first, then check your work.
Examiner trap
Since the sign bit (MSB) is , invert all bits and add to find the magnitude, then attach a negative sign.
This Number Representation and Arithmetic previous year question is Q7 of the GATE CSE 2016 Set 1 paper. Find more GATE CSE PYQs on Number Representation and Arithmetic in Digital Logic, or browse all GATE CSE PYQs.
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Number Representation and Arithmetic has 33 GATE CSE PYQs across 20 papers from 2012 to 2026. 11 of them are 1-mark NAT questions like this one, and it is the only one in GATE CSE 2016 Set 1.
How GATE tests Number Representation and ArithmeticIndependent practice explanation verified by the GateAI team. GATE is conducted by the IITs; question text follows the official paper.