Difficulty: Easy
Correct Answer: 1001111110
Explanation:
Introduction / Context:Binary arithmetic underlies computer operations at the hardware level. This exercise tests accurate subtraction of two unsigned binary numbers and recognition of the correct result among plausible distractors.
Given Data / Assumptions:
Concept / Approach:We can subtract using either direct binary column subtraction with borrows or convert to decimal for a cross-check. Converting to decimal often provides a quick sanity check before re-encoding the result back to binary.
Step-by-Step Solution:
Convert minuend: 1110101010₂ = 1*512 + 1*256 + 1*128 + 0*64 + 1*32 + 0*16 + 1*8 + 0*4 + 1*2 + 0*1 = 938. Convert subtrahend: 100101100₂ = 1*256 + 0*128 + 0*64 + 1*32 + 0*16 + 1*8 + 1*4 + 0*2 + 0*1 = 300. Subtract in decimal: 938 − 300 = 638. Convert 638 back to binary: 638 = 512 + 126 = 512 + 64 + 32 + 16 + 8 + 4 + 2 = binary 10 0111 1110 → 1001111110₂.Verification / Alternative check:Perform column-wise binary subtraction with borrows; the final bits match 1001111110, confirming the decimal cross-check result.
Why Other Options Are Wrong:
1001011110: close-looking distractor but equals 638 − 32 = 606, not our difference. 0110100001 and 1111000001: mismatched magnitudes; converting to decimal shows incorrect values. None: invalid because a correct option is present.Common Pitfalls:Misaligning bit positions due to different operand lengths; always align the least significant bits. Also, forgetting borrows in binary column subtraction yields off-by-powers-of-two errors.
Final Answer:1001111110
Discussion & Comments