Two’s complement addition (8-bit): Add 11110010 and 11110011. First identify each 8-bit number's decimal sign and magnitude, then compute their decimal sum.

Introduction / Context:Two’s complement is the dominant signed binary representation used by processors. Mastery involves recognizing negative values, converting between binary and decimal, and performing addition with correct overflow interpretation.

Given Data / Assumptions:

• Word size: 8 bits.
• Operands: 11110010 and 11110011.
• Interpretation: two’s complement signed integers.

Concept / Approach:For two’s complement: if the MSB is 1, the value is negative and equals the negative of the two’s complement magnitude. To find magnitude: invert bits, add 1. Addition of two’s complement numbers uses ordinary binary addition; discard any carry beyond 8 bits, then interpret the result with sign bit.

Step-by-Step Solution:

Verification / Alternative check:Decimal arithmetic confirms –27. The sign bit of 11100101 is 1 and magnitude check yields 27, consistent with –27. No signed overflow occurred here because adding two negatives cannot overflow into positive in 8-bit unless magnitude exceeds range, which it does not (range is –128 to +127).

Why Other Options Are Wrong:

• –113 and –114; 227: Magnitudes misread and sum sign incorrect.
• –27 and –13; 40: First operand’s interpretation wrong; sum inconsistent.
• –11 and –16; –27: Operand magnitudes misdecoded.

Common Pitfalls:Forgetting to invert then add 1 when decoding negatives; mishandling end carry; misinterpreting the sign bit after addition.

Final Answer:–14 and –13; –27