täissummaattori

A täissummaattori, often translated as a full adder, is a fundamental digital logic circuit that performs the addition of three single binary digits. Unlike a half adder, which only adds two bits and produces a sum and a carry-out, a full adder incorporates a third input, typically referred to as the carry-in. This carry-in bit allows for the cascading of full adders to create circuits capable of adding binary numbers of any length.

The full adder has three inputs: A, B, and Cin (carry-in). It produces two outputs: S (sum) and Cout (carry-out). The sum output (S) is 1 if an odd number of the inputs (A, B, Cin) are 1, and 0 otherwise. This can be expressed by the XOR operation: S = A ⊕ B ⊕ Cin. The carry-out output (Cout) is 1 if two or more of the inputs are 1, and 0 otherwise. This can be expressed as: Cout = (A ⋅ B) + (A ⋅ Cin) + (B ⋅ Cin), or alternatively as Cout = (A ⋅ B) + Cin ⋅ (A ⊕ B).

Full adders are essential building blocks in digital electronics, particularly in arithmetic logic units (ALUs) within microprocessors and other computing devices. By connecting multiple full adders in series, where the carry-out of one adder becomes the carry-in of the next, complex binary addition operations can be performed efficiently. This ripple-carry adder design is a straightforward way to implement multi-bit addition.