Also a euphemism for stealing.

"I borrowed some things from the grocery store."

Borrow is the opposite of carry. It occurs when breaking through the lower bound of modulo arithmetic.

In computer science: when subtracting one unsigned register from a similar-sized unsigned register, a borrow occurs when the result is negative. A borrow flag is set when this occurs - it is cleared when a subtraction does not result in a negative number. The borrow flag is useful for multiple-word arithmetic: given a 2-word value AB (register A holding the most significant word, register B being the least significant word), to subtract a 1-word value C: First subtract C from B. If this causes a borrow, decrement A. If the decrement causes a borrow also, then the overall result is negative and is stored in 2's complement form in AB, otherwise the result is positive (or zero) and is correctly stored in unsigned form in AB.

Because of this, many machine code instruction sets include not only a 'subtract' instruction, but also a 'subtract with borrow' instruction. To subtract a 3-word value DEF from ABC, then, the pseudocode would look something like:
clear the borrow flag
subtract with borrow, F from C
subtract with borrow, E from B
subtract with borrow, D from A
(The first two instructions could be replaced with a single regular 'subtract' instruction... the verbosity is intentional, to illustrate the pattern that is at work here.) If the borrow is set after all that, the result is negative.

Also called unsigned underflow.

Bor"row (?), v. t. [imp. & p. p. Borrowed (#); p. pr. & vb. n. Borrowing.] [OE. borwen, AS. borgian, fr. borg, borh, pledge; akin to D. borg, G. borg; prob. fr. root of AS. beorgan to protect. 95. See 1st Borough.]

1.

To receive from another as a loan, with the implied or expressed intention of returning the identical article or its equivalent in kind; -- the opposite of lend.

2. Arith.

To take (one or more) from the next higher denomination in order to add it to the next lower; -- a term of subtraction when the figure of the subtrahend is larger than the corresponding one of the minuend.

3.

To copy or imitate; to adopt; as, to borrow the style, manner, or opinions of another.

Rites borrowed from the ancients. Macaulay.

It is not hard for any man, who hath a Bible in his hands, to borrow good words and holy sayings in abundance; but to make them his own is a work of grace only from above. Milton.

4.

To feign or counterfeit.

"Borrowed hair."

Spenser.

The borrowed majesty of England. Shak.

5.

To receive; to take; to derive.

Any drop thou borrowedst from thy mother. Shak.

To borrow trouble, to be needlessly troubled; to be overapprehensive.

Bor"row, n.

1.

Something deposited as security; a pledge; a surety; a hostage.

[Obs.]

Ye may retain as borrows my two priests. Sir W. Scott.

2.

The act of borrowing.

[Obs.]

Of your royal presence I'll adventure The borrow of a week. Shak.