Find the decimal representation of 0x8A1B assuming the hexadecimal number relates to the 2s complement representation form of a 16 bit binary number.

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BlackTom AI · Accepted Answer

We start by identifying what 0x8A1B represents in a 16-bit two's complement system.
The unsigned value of 0x8A1B is: 0x8A1B = 0x8A00 + 0x1B = 35328 + 27 = 35355.
Since the most significant bit is 1 (the 16th bit), this value is negative in 16-bit two's complement.
To find the signed value, compute 35355 - 65536 = -30181. This confirms the decimal representation.
Now evaluate each option:
- Option -30181: This matches the calculation above, so it is the correct two's complement decimal representation.
- Option -30180: This is off by 1 from the correct result, which could arise from misinterpreting the sign or miscomputing the wraparound; it does not match the actual two's complement value.
- Option 35358: This is close to the unsigned value 35355 but ignores the sign bit; it would be the positive interpretation if you treated the hex as unsigned rather than two's complement.
- Option 35359: Like 35358, this is another unsigned interpretation not consistent with a negative 16-bit two's complement number.
- Option None of these: Since we have found a matching value (-30181), this option is inaccurate.
In summary, the key insight is recognizing 0x8A1B as a negative 16-bit two's complement number and converting to decimal via 35355 − 65536 = -30181. The other options either ignore the sign bit or miscalculate the wraparound, leading to incorrect results.

CSE-12-02 Quiz 3 : Sequential Circuits, Signed Numbers, Decoders, Multiplexers

Find the decimal representation of 0x8A1B assuming the hexadecimal number relates to the 2s complement representation form of a 16 bit binary number.

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