Addsubtract

Addsubtract is a term used to describe a dual-function arithmetic capability in digital logic and computing, where a single unit can perform either addition or subtraction on binary numbers. In practice, addsubtract is often implemented as an add-subtractor within an arithmetic logic unit (ALU), controlled by a mode signal that selects the operation.

Mechanism

A common hardware realization uses a standard binary adder with the second operand inverted when subtraction is chosen. If the operation mode is SUB = 0, the circuit computes A + B. If SUB = 1, it computes A − B by feeding B′ = B XOR SUB and setting the carry-in to SUB, effectively performing A + (NOT B) + 1 in two’s complement form. This approach allows reusing a single adder hardware block to perform both operations, reducing circuit area and complexity.

Overflow and carry

For unsigned arithmetic, the carry-out of the addition indicates a result that wraps around. For signed arithmetic in two’s complement representation, overflow is detected by examining the carry into and out of the most significant bit or by comparing sign bits of operands and result. Proper flag logic is essential for correct interpretation of results in both addition and subtraction modes.

Variants and applications

Addsubtract capabilities are central to many processors’ ALUs and are also found in scientific calculators and digital signal processing, where compact and fast arithmetic units are valued. Some architectures implement separate subtractors or more elaborate sign-aware units, but the addsubtract approach remains a foundational technique for achieving dual operations with shared hardware.

See also

Arithmetic logic unit, Two’s complement, Overflow detection, Adder-subtractor.