Two's-complement calculation: Find the 2's-complement of 00001111 (8-bit representation).

Introduction / Context:
Two's-complement is the dominant signed number encoding in digital systems. It is formed by inverting all bits (one's-complement) and then adding 1 to the least significant bit.

Given Data / Assumptions:

• Original byte: 00001111 (decimal 15).
• We want its 2's-complement in 8 bits.

Concept / Approach:
2's-complement(X) = (~X) + 1. For 00001111: one's-complement is 11110000; adding 1 yields 11110001.

Step-by-Step Solution:

Verification / Alternative check:
Adding the number and its 2's-complement gives 00000000 with a carry out, confirming correctness.

Why Other Options Are Wrong:

Common Pitfalls:
Stopping at inversion without adding 1, or changing bit width inadvertently.

Final Answer:
11110001