Two's-complement representation: Find the 2's complement (binary) needed to represent –(110110₂).

Introduction / Context:
Here we practice forming a two's-complement pattern for a negative value. When asked for the 2's complement of a positive binary pattern, the result is the bit pattern that represents its negative in two's-complement arithmetic.

Given Data / Assumptions:

• Unsigned magnitude given: 110110₂.
• Goal: produce the two's-complement bit pattern that corresponds to –110110₂.
• Assume a fixed width just large enough to hold the bits shown (6 bits here).

Concept / Approach:
To form –N in two's-complement: take N, invert all bits (one's complement), then add 1. Ensure you keep the same bit width while performing the operation.

Step-by-Step Solution:
Start with N = 110110.Invert bits ⇒ 001001.Add 1 ⇒ 001001 + 1 = 001010.Therefore, two's-complement pattern for –110110₂ is 001010₂.

Verification / Alternative check:
Check by addition: 110110 + 001010 = 1000000 (carry out of the 6-bit range). Dropping the carry in fixed width yields 000000, confirming that 001010 is the additive inverse of 110110 in 6-bit two's-complement.

Why Other Options Are Wrong:
110100₂, 101010₂, 001001₂, 110111₂: Each fails either the invert-plus-one rule or the additive-inverse check (sum within 6 bits must be 000000).

Common Pitfalls:
Forgetting the final +1, changing the bit width mid-calculation, or misreading the order of bits during inversion.

Final Answer:
001010₂