In eight bit two's complement notation write down the binary for -125

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Question restatement: In eight-bit two's complement notation, write down the binary for -125. The answer choices are: -125 is too large to represent in 8 bits 2's complement; 1000 0011; 0111 1101; 1000 0010.

Option 1: -125 is too large to represent in 8 bits 2's complement. This is incorrect. Eight-bit two's complement can represent integers from -128 to +127, so -125 is well within the range.

Option 2: 1000 0011. This is the correct representation of -125 in 8-bit two's complement. Explanation: 125 in binary is 0111 1101. Inverting bits gives 1000 0010, and adding 1 yields 1000 0011, which indeed encodes -125 in two's complement.

Option 3: 0111 1101. This binary pattern is the positive number +125, not -125. It corresponds to the unsigned value 125 and the two's complement interpretation would be +125, which is not what is asked.

Option 4: 1000 0010. This value corresponds to -126 in 8-bit two's complement. You can check by taking 1000 0010, subtracting from 256 yields 256 - 130 = 126, confirming its representation as -126 rather than -125.

Summary of reasoning: The correct encoding for -125 in 8-bit two's complement is found by taking the binary of 125, inverting, then adding 1, which yields 1000 0011. The other options either misrepresent the sign (positive 125), misstate the range, or correspond to a different negative value (-126).

4520_COMP_SCI_X_0005 Week 3 Quiz

In eight bit two's complement notation write down the binary for -125

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