Which subtractor is specifically designed to generate a difference and has borrowing capability?

The choice that accurately identifies the subtractor designed to generate a difference and possesses borrowing capability is indeed the full subtractor.

A full subtractor takes three inputs: two significant bits (the minuend and subtrahend) and a borrow input from a previous subtraction operation. It produces two outputs: the difference between the minuend and subtrahend, and a borrow output that indicates whether the minuend was smaller than the subtrahend. This functionality allows it to handle situations where a loan is needed for the subtraction process, making it essential in multi-bit binary subtraction.

In contrast, a half subtractor only processes two bits without the capability to account for any borrowing from a previous bit, limiting its application to a single digit of a binary number. The other options, such as the quarter subtractor and adder, do not fit the definition of a borrowing capable subtractor, as a quarter subtractor is not a standard term used in digital electronics, and an adder is designed to perform addition, not subtraction. Thus, the full subtractor is specifically built to address the complexities of subtraction where borrowing is necessary.