In an 8-bit two's-complement system, what is the largest-magnitude negative number (i.e., the minimum representable value) that can be stored?

Introduction / Context:
Two's-complement encoding is the standard for signed integers in digital systems. Understanding its numeric range avoids overflow and sign errors in embedded and computer systems.

Given Data / Assumptions:

• Word size: 8 bits.
• Signed representation: two's complement.

Concept / Approach:

For an n-bit two's-complement integer, the value range is from -2^(n-1) to +2^(n-1) - 1. For n = 8, the range is -128 to +127.

Step-by-Step Solution:

Verification / Alternative check:

Binary 1000 0000 in two's complement equals -128. No other 8-bit pattern is more negative.

Why Other Options Are Wrong:

• -256 and -255: not representable in 8 bits two's complement.
• -127: not the most negative; it is closer to zero than -128.
• 0: not negative.

Common Pitfalls:

Interpreting “greatest negative” as closest to zero (e.g., -1); in range questions, it means the minimum value (most negative), which is -128 for 8-bit two's complement.

Final Answer:

- 128