Below is a two’s compliment binary number:

11110100

Please write it’s base 10 value in the space provided.

Question

Below is a two’s compliment binary number:

11110100

Please write it’s base 10 value in the space provided.

BlackTom AI · Accepted Answer

A two’s complement byte with a leading 1 represents a negative number; convert by finding the magnitude via two’s-complement inversion and addition.

1) Relevant knowledge points and concepts
- Two’s complement representation: for an n-bit value, the most significant bit (MSB) has weight -2^(n-1); the remaining bits have positive weights 2^(n-2) ... 2^0. 
- Alternatively, to get the magnitude of a negative two’s-complement number, invert all bits (one’s complement) and add 1; the result is the positive magnitude in binary.

2) Step-by-step reasoning
Given 11110100 (8 bits).
Method A (invert + 1):
- Invert bits (one’s complement): 11110100 -> 00001011
- Add 1: 00001011 + 00000001 = 00001100

3) Intermediate calculations shown
- 00001100 in decimal = 2^3 + 2^2 = 8 + 4 = 12
- Since the original had MSB = 1 (negative), the value is -12.

Method B (weighted sum using sign-bit weight):
- Weights: 128, 64, 32, 16, 8, 4, 2, 1
- Sum positive bits except sign: 64 + 32 + 16 + 4 = 116
- Include sign-bit as negative: -128 + 116 = -12

4) Why the correct answer is correct
Both methods agree: the two’s complement rules produce magnitude 12 with a negative sign because the MSB is 1. The invert-plus-one method explicitly finds the positive magnitude; the weighted-sum method applies the MSB negative weight directly. Both yield -12.

5) Why other interpretations are incorrect
Interpreting 11110100 as an unsigned byte gives 244 (128+64+32+16+4), which is incorrect for two’s complement signed interpretation. Using one’s complement without adding 1 would yield −(00001011) = −11, which is wrong because two’s complement requires the +1 step.

6) Conclusion
The two’s complement value of 11110100 is -12, matching the provided answer: -12.

Below is a two’s compliment binary number: 11110100 Please write it’s base 10 value in the space provided.Short answer

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