How many times is a borrow required to solve the below given equation?
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How many times is a borrow required to solve the below given equation?
A = 11101 - 01110
Show answer & explanation
Answer: B. 1
In binary subtraction of 11101 - 01110, we work right-to-left column by column. Most columns can be subtracted directly (1-0=1, 1-1=0, 0-0=0), but at position 2 (from right, 0-indexed), we encounter 0-1, which requires exactly one borrow from position 3. After borrowing, 0 becomes 10 (binary 2), and 10-1=1. The result is 01111 (decimal 15).
Step-by-step Derivation:
Binary subtraction of 11101 - 01110:
11101
- 01110
Column-by-column (right to left, position 0 to 4):
- Position 0: 1 - 0 = 1 (no borrow needed)
- Position 1: 0 - 1 = ? (BORROW REQUIRED from position 2)
After borrow: 10 - 1 = 1, position 2 becomes 0 - Position 2: 0 - 1 = ? Already borrowed, becomes: 1 - 1 = 0
- Position 3: 1 - 1 = 0 (no borrow needed)
- Position 4: 1 - 0 = 1 (no borrow needed)
Result: 01111
Total borrow operations: 1