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

Question

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.

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

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