AddierSubtrahierEinheit

The AddierSubtrahierEinheit, literally “Addition-Subtraction Unit” in German, is a modular digital circuit used to perform binary addition and subtraction on fixed-width operands. It is a common component of arithmetic logic units (ALUs) in CPUs and microcontrollers. The unit accepts two n-bit inputs, A and B, a mode control M (0 for addition, 1 for subtraction), and an optional carry-in.

In addition mode, the unit computes S = A + B with Cin typically set to 0. In subtraction mode, it computes A - B by inverting B and setting Cin to 1, effectively performing A + (~B) + 1 (two’s complement). The core yields an n-bit sum S and status outputs such as carry-out and overflow, which indicate unsigned and signed conditions respectively.

Typical implementations use a conventional n-bit adder as the core. B is selected as B' = B XOR M, and Cin = M, so a single adder handles both operations. Extensions may include carry-lookahead adders for speed or pipelining for throughput, and flag logic to support comparison and conditional branching.

Used in digital processors, embedded systems, and DSPs, the AddierSubtrahierEinheit supports both signed and unsigned arithmetic depending on how flags are interpreted. Variants exist with different widths, or as part of larger ALUs with additional logic for multiplication and division.

See also Adder, Subtractor, Arithmetic Logic Unit, Two’s complement, Carry lookahead adder.