Number system

A number system is a system that encodes a number. Number systems divide into two primary groups:


 * Additive number systems, where the value of each digit is constant and in which the number expressed is the sum of all digits. Common variants include:
 * Strictly additive systems, where only addition is used. Examples include the Greek numerals
 * Subtractive systems, where a digit can also mean "subtract from the next number". Examples include the Roman numerals
 * Strictly subtractive systems, where only subtraction is used.
 * Non-standard additive systems.
 * Positional number systems, where the value of each digit is multiplied by a coefficient based on its position in the number. The values received in this way are then added to express the number. Each positional number system has a base or radix the powers of which dictate the values of the coefficients in the position. The LSD (Least Significant Digit) has a value of base0=1., the second-to-last digit has a value of base1, the third-to-last base2 and so on until the MSD (Most Significant Digit). The most common variants include:
 * Standard positional number systems, where the base is a natural number greater than 1
 * Negative bases, where the base is a negative integer
 * Balanced bases, where the digits also represent negative values rather than just natural
 * Bijective bases, which reject the use of 0 and use the next available digit instead. Common in modern alphabet-based numeration.
 * Skew bases, which slightly change the values represented by 10, 100, 1000... (in their respective bases)
 * Non-integer bases.