Kaksinkomplementin

Kaksinkomplementin, known in English as two's complement, is a mathematical operation on binary numbers and a way to represent signed integers. It is the most common method for representing signed integers on computers. The term "kaksinkomplementin" itself is Finnish.

The purpose of kaksinkomplementin is to simplify arithmetic operations, particularly subtraction, which can be performed using the same circuitry as addition. In a kaksinkomplementin system, a negative number is represented by inverting all the bits of its positive counterpart and then adding one. For example, to find the kaksinkomplementin of a binary number, you first flip all the bits (0s become 1s, and 1s become 0s). Then, you add 1 to the resulting number.

This method allows for a straightforward way to perform subtraction. Instead of subtracting a number B from a number A, one can add the kaksinkomplementin of B to A. This simplifies the design of arithmetic logic units (ALUs) within computer processors. The most significant bit (MSB) in a kaksinkomplementin representation typically indicates the sign of the number: 0 for positive and 1 for negative.

Kaksinkomplementin systems have a unique property: the number of negative representations is one greater than the number of positive representations for a given number of bits. For instance, with 8 bits, you can represent numbers from -128 to +127. The zero is represented uniquely as all zeros. This asymmetry is a consequence of the method and ensures that the range of representable numbers is balanced around zero.