Radices

Overview

The radix is the number of unique digits used to represent numbers in a positional numeral system. Most commonly used systems tend to be binary ($2$-base), octal ($8$-base), decimal ($10$-base), and hexadecimal ($16$-base).

Scientific Notation

Scientific notation is a means of expressing non-zero values in base $b$ as $m\times b^n$. The number $m$ is called the significand (or mantissa). The number $n$ is called the exponent. Scientific notation is most commonly used in base $10$.

Fixed-Point

Fixed-point refers to the representation of fractional numbers by storing a fixed number of digits of their fractional part. The most common variants of fixed-point arithmetic use base $10$ and base $2$.

The precision of a fixed-point type refers to the total number of significant digits in the whole number. The scale is the count of decimal digits in the fractional portion of the type. For example, number $1.23$ has precision $3$ and scale $2$. Alternatively, we view is as integer $123$ with scaling factor ${10}^{-2}$.

Floating-Point

Floating-point refers to the representation of fractional numbers by storing a significand (a signed sequence of a fixed number of digits in some base) multiplied by an integer power of that base. The most common variants of floating-point are decimal (base $10$) and binary (base $2$).

The precision of a floating-point type refers to the number of bits found in the fractional field (plus $1$ to account for the implicit leading bit).

Floating-point is an example of scientific notation.