Radix point (radix character)
Symbol that separates the integer part from the fractional part of a number in a given base; commonly a decimal point or comma, with variants for binary, octal, hexadecimal and locale rules.
Overview
In mathematics and computing, a radix point (sometimes called a radix character) marks the boundary between the whole-number portion and the fractional portion of a positional numeral. In everyday base‑10 notation it is often called the decimal point; in base‑2 it is called the binary point. The radix point does not itself have numerical value but indicates the place values of digits to its left (positive powers) and to its right (negative powers).
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Definition and notation
Formally, a numeral written in base b with digits d_k...d_1 d_0 . d_{-1} d_{-2} ... represents the value Σ d_i b^i, where the radix point separates nonnegative and negative exponents. Common symbols used for the radix point include a full stop or dot (.), a comma (,), or a raised dot or centered dot in some historical or technical contexts. Which symbol is used depends on typographical convention and locale.
Names and base-specific terms
The general term "radix point" applies to any base. Specific names arise from the base: "decimal point" for base 10, "binary point" for base 2, "octal point" for base 8, and so on. When writing numbers in hexadecimal or other bases the same concept applies: digits left of the radix are multiplied by positive powers of the base, digits to the right by negative powers. For example, the number 1200.25 in decimal equals 1200 + 25×10-2, and the binary number 101.1 equals 5.5 in decimal.
Examples and simple uses
- Decimal example: 1200.25 = 1200 + 0.25 = 1200 + 25/100.
- Binary example: 10.11 (base 2) = 2 + 0.75 (decimal) because 0.11₂ = 1/2 + 1/4.
- Fixed‑point formats hold an implicit radix point at a known position; floating‑point formats store a significand and exponent to represent a movable radix point.
History and typographical variants
The symbol chosen for the radix point has varied by region and period. Many English-speaking countries use a dot; many continental European countries use a comma as the standard radix separator. Historical texts and technical manuals have also used middle dots or spaces. Standards for scientific and technical communication often specify one convention or the other to avoid ambiguity in international contexts.
Computing, parsing, and important distinctions
In computing, the radix point is important for lexical analysis and numeric parsing. Programming languages typically expect a particular character as the radix marker (commonly a dot), and some languages or libraries accept localized separators. Floating‑point arithmetic treats the radix point as variable through exponent encoding; fixed‑point arithmetic keeps it at a constant position. When converting between bases, digits on either side of the radix must be scaled by powers of the source base to obtain the equivalent representation in the target base. For further technical background see entries on integers and fractions, and practical notes about base‑10 notation at base ten.
Notable practical issues include locale mismatch (where printed numbers use a comma but software expects a dot), typographical spacing around the radix marker in tables, and the representation of repeating fractions that extend infinitely to the right of the radix in a given base.
Questions and answers
Q: What is a radix point?
A: A radix point is a symbol used to separate whole numbers from fractions.
Q: Can you give an example of a number with a radix point?
A: Yes, the number 1200.25 represents an integer of 1200 with a fractional part of 25, and these are separated with a decimal point.
Q: Is the radix point the same in all number bases?
A: Yes, the radix point is the umbrella term for this point in all bases.
Q: What is the "binary point"?
A: The "binary point" is the radix point used for base 2.
Q: Is the radix point always represented by a decimal point?
A: No, the radix point can vary. In most English-speaking countries, the radix point is usually a small dot (.), but other languages can use different notation such as a comma (,) instead.
Q: Why is the decimal point called the decimal point?
A: The decimal point is called so because it is used in base 10 notation.
Q: What does the radix point separate in a number?
A: The radix point separates whole numbers (integers) from fractions.
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AlegsaOnline.com Radix point (radix character) Leandro Alegsa
URL: https://en.alegsaonline.com/art/80787