Binary subtraction with borrowing through zeros: When a borrow is needed from a bit position that contains 0, you must borrow from the next more significant position that contains 1; every 0 passed becomes 1 after the borrow chain, and the final position borrowed from becomes 0. Judge this rule.

Introduction / Context:
Borrowing in binary subtraction follows patterns similar to decimal subtraction, but with base 2. Understanding the borrow chain through consecutive zeros is essential for hand calculations and for reasoning about hardware subtractors.

Given Data / Assumptions:

• Base-2 subtraction using standard borrow (no complements method in this explanation).
• Minuend and subtrahend aligned by bit significance.
• Borrow propagates from more significant to less significant positions.

Concept / Approach:
When the current bit of the minuend is 0 and you need to subtract 1 (or a higher sub-bit), you cannot subtract without a borrow. If the immediate higher bit is also 0, you move left until a 1 is found. That 1 becomes 0, and every intermediate 0 becomes 1 because each received a borrow and then passed a borrow to the next lower bit.

Step-by-Step Solution:

Verification / Alternative check:
Example: 10000 − 00001. To subtract at the LSB, you search left until the MSB; it becomes 0, all zeros in between become 1, and the final result is 01111.

Why Other Options Are Wrong:
“Invalid” contradicts the fundamental base-2 borrowing rule. The octal/BCD qualifiers are irrelevant to binary subtraction mechanics.

Common Pitfalls:
Forgetting to flip each intermediate 0 to 1 during the borrow chain, which leads to errors in multiple adjacent positions.

Final Answer:
Valid