Which type of adder is specifically designed to add two binary digits and produce a sum and borrow signal?

The type of adder specifically designed to add two binary digits and produce a sum and a borrow signal is the full adder. A full adder takes three inputs: two significant bits of the binary numbers being added and an incoming carry (or borrow) bit from the previous less significant stage. In addition to providing the sum of these bits, it also generates an output carry (or borrow) when the total exceeds what can be represented in a single binary digit.

This capability allows a full adder to perform addition in multi-bit binary numbers by cascading multiple full adders together. Each stage accounts for carry-in and calculates the carry-out, enabling efficient binary addition in broader contexts.

In contrast, a half adder can only add two bits together and produces a sum and a carry-out, but it lacks the ability to include an incoming carry from a previous stage, and thus does not handle borrow operations. A quarter adder is not a recognized term in standard binary arithmetic. Meanwhile, a binary subtractor is primarily designed for subtraction tasks and does not provide a sum; it deals with differences and borrows in a context distinct from addition. Consequently, the full adder is the correct answer as it encompasses the needed functions.