Radixpunkt

Radixpunkt is the term used in numeral systems to describe the separator between the integer and the fractional part of a number. It marks the boundary between digits that carry powers of the base (radix) and those that carry negative powers. The base b determines the value of each digit’s position, with positions to the left of the radixpunkt weighing b^k and positions to the right weighing b^−n. The radixpunkt, therefore, is the dividing line between whole-number and fractional parts in any positional notation.

In everyday usage, the decimal point is the radixpunkt in base 10. For example, 123.456 uses the radixpunkt between 123 and 456. In other bases, the same concept applies: 1011.01_2 equals 11.25 in decimal, and FF.AA_16 equals 255 plus a fractional part of about 0.666... in decimal.

The term is neutral with respect to locale and base. In German, the everyday decimal separator is often a comma (Komma) for dezimalzahlen, but the technical concept of a central separator between integer and fractional parts is still the radixpunkt. In English, “decimal point” is common, while the general concept across bases is sometimes referred to as the radix point.

In computing, the radixpunkt features in two main contexts. Fixed-point arithmetic uses a fixed radixpunkt, whereas floating-point arithmetic represents numbers with an exponent that effectively moves the point, enabling a wide range of magnitudes without changing the base representation.