Borrow ($b_i$)

In positional subtraction, a higher place supplies one unit of its place value when the current place cannot subtract the requested digit. In binary representation, subtraction of one, a low bit toggles at every operation and the borrow continues through each zero bit, stopping at the first one bit. Thus decrementing a binary counter toggles position $i$ exactly when all less significant bits were zero. This is the downward-counting counterpart of a carry propagating through one bits during incrementing.