Binary subtraction basics Compute the result of 111₂ − 001₂ and express the answer in binary.

Introduction / Context:Binary subtraction mirrors decimal subtraction but with base 2. Recognizing basic patterns such as subtracting 1 from a number simplifies mental computation and checking of results.

Given Data / Assumptions:

• Minuend: 111₂ (which equals 7 decimal).
• Subtrahend: 001₂ (which equals 1 decimal).
• No borrow issues across more than one bit in this simple case.

Concept / Approach:Since 111₂ is all ones, subtracting 001₂ simply clears the LSB and leaves the higher bits unchanged, equivalent to 7 − 1 = 6 decimal. Convert back to binary after subtraction to confirm.

Step-by-Step Solution:

Verification / Alternative check:Perform column-wise binary subtraction: from right to left, 1−1=0; next bits 1−0=1; next 1−0=1 → 110.

Why Other Options Are Wrong:

• 100: equals 4, not 6.
• 111: equals the original minuend (no subtraction performed).
• 001: equals 1, the subtrahend.

Common Pitfalls:Attempting unnecessary borrows when subtracting 1 from an odd number ending in 1.

Final Answer:110