Compute –11 + (–2) using 8-bit two’s complement. Which 8-bit two’s-complement result is obtained?

Introduction / Context:
Binary arithmetic with signed numbers relies on two’s complement encoding. This question checks your ability to encode negatives and perform binary addition correctly within a fixed word size (8 bits).

Given Data / Assumptions:

• Operands: –11 and –2.
• Word length: 8 bits.
• Two’s complement arithmetic; discard carry out of MSB.

Concept / Approach:
To represent –N in two’s complement: write N in binary, invert all bits, then add 1. Add using binary rules; the carry beyond bit 7 is dropped. Interpret the final 8 bits as two’s complement.

Step-by-Step Solution:

Verification / Alternative check:
Decimal check: –11 + –2 = –13; result encoding 1111 0011 corresponds to –13 in 8-bit two’s complement. Range –128…+127 supports this result without overflow.

Why Other Options Are Wrong:

• 1110 1101 / 1110 1001 / 1111 1001: These bit patterns decode to other negative values (not –13) and do not match the arithmetic.

Common Pitfalls:
Not discarding the end carry; forgetting the invert+1 rule; mixing sign-magnitude with two’s complement decoding.

Final Answer:
1111 0011