Binary subtraction check – is 1011 (base 2) minus 0111 (base 2) equal to 1000 (base 2)?

Introduction / Context: This problem verifies binary subtraction accuracy. As with decimal, you may subtract bit-by-bit with borrows or convert to two’s-complement addition for a systematic approach. We compare the given claim to the computed result.

Given Data / Assumptions:

• Operands: 1011 (11 decimal) and 0111 (7 decimal).
• Unsigned comparison; no modular wrap unless explicitly specified.
• Goal: test if the difference equals 1000.

Concept / Approach: Compute 11 − 7 = 4 (decimal). The correct binary for 4 is 0100 (or simply 100). The proposed 1000 equals 8 (decimal), which is not the correct difference. Therefore, the statement is false.

Step-by-Step Solution:

Verification / Alternative check: Two’s complement: 1011 + (two’s complement of 0111 = 1001) = 10100. Discard carry beyond 4 bits → 0100, matching the direct subtraction result, so 4 is confirmed.

Why Other Options Are Wrong: Borrow inhibition or signed mode does not make 11 − 7 equal 8. Modulo wrap would require a specified fixed width and still would not yield 1000 as the canonical result here.

Common Pitfalls: Mixing up borrow steps or misaligning bits. Always line up bits and track borrows carefully.

Final Answer: Incorrect