Evaluate the claim for eight-bit two’s-complement representation: “The representation of −110 (decimal) in 8-bit two’s complement is 11110111.” Is this statement valid?

Introduction / Context:
Two’s-complement is the dominant representation for signed integers in digital systems. Verifying a negative encoding requires converting the positive magnitude to binary, inverting bits, and adding 1, then checking the result.

Given Data / Assumptions:

• We need the 8-bit two’s-complement encoding of −110 (decimal).
• Range of 8-bit two’s complement is −128 to +127.
• Binary conversion and two’s-complement steps are applied precisely.

Concept / Approach:
Find +110 in 8 bits, invert all bits, then add 1. If the final pattern matches the claim (11110111), the statement is correct; otherwise it is incorrect. Also, interpret 11110111 to see what decimal value it represents to cross-check.

Step-by-Step Solution:
1) +110 in 8-bit binary: 110 = 64 + 32 + 8 + 4 + 2 → 01101110.2) Invert bits: 10010001.3) Add 1: 10010001 + 1 = 10010010.4) Therefore, −110 encodes as 10010010, not 11110111.5) Interpret 11110111: as two’s complement, value = −(~11110111 + 1) = −(00001000 + 1) = −9.

Verification / Alternative check:
Compute 256 − 110 = 146; 146 in hex is 0x92 which is 10010010, matching the step-by-step conversion.

Why Other Options Are Wrong:
“Correct” contradicts the computed code. The options about one’s-complement or sign-magnitude are red herrings; the question explicitly concerns two’s complement.

Common Pitfalls:
Mistaking bit order; forgetting to add 1 after inversion; mixing up representations like one’s complement or sign-magnitude with two’s complement.

Final Answer:
Incorrect