Category: Twos Complement -125

In eight bit two's complement notation what is the binary for -125

Question

Category: Twos Complement -125

In eight bit two's complement notation what is the binary for -125

BlackTom AI · Accepted Answer

To determine the eight-bit two's complement representation of -125, we first recall how negative numbers are encoded in this scheme. In 8-bit two's complement, the range is from -128 to 127, so -125 is representable. A common method is:
1) Find the binary of the positive magnitude: 125 = 01111101 in 8 bits.
2) Invert all bits (bitwise NOT): 10000010.
3) Add 1 to obtain the two's complement: 10000010 + 1 = 10000011.
Thus, the correct encoding is 10000011.

Option-by-option analysis:
Option A: 10000011. This matches the computed two's complement representation for -125, so it is correct.
Option B: 10000010. This is only the bitwise NOT of 01111101 (the one's complement), not the final two's complement value after adding 1. Therefore it represents -126 in some schemes, but not -125 in 8-bit two's complement.
Option C: 01111101. This is the binary for +125, not -125, so it is incorrect for negative 125.
Option D: -125 is too large to represent in 8 bits 2's complement. This statement is false because the 8-bit two's complement range includes -128 to 127, which does include -125.

4520_COMP_SCI_X_0005 Practice Exam

Category: Twos Complement -125 In eight bit two's complement notation what is the binary for -125

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