Numeral/Numerical/Number Systems/Representations/Notations
- is a writing system for expressing numbers (mapping numbers to characters)
- i.e. it defines how we represent an abstract number into a sequence of symbols/characters, and where the number of distinct symbols allowed is fixed
- e.g. the abstract number twelve is represented as a sequence of symbols 12 (1 followed by 2). The number of distinct symbols used in this numeral system is ten (i.e. 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9)
- similar to the character set, but different
Numeral/Number Systems/Representations/Notations - Types
|
Type |
Alias |
# of Distinct Symbols |
Symbols Commonly Used |
|---|---|---|---|
|
64 |
a subset of ASCII characters | ||
|
64 |
a variant of Base64 Notation used in URLs | ||
|
Base60 |
Sexagesimal |
60 |
originated with ancient Sumerians in the 3rd millennium BC, and was passed down to the Babylonians |
|
32 | |||
|
Hexadecimal |
16 |
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F | |
|
Base12 |
Duodecimal |
12 | |
|
Decimal |
10 |
0, 1, 2, 3, 4, 5, 6, 7, 8, 9 | |
|
Octal |
8 | ||
|
Quaternary |
4 | ||
|
Binary |
2 |
0, 1 | |
|
Unary Tally Marks |
1 |
1 | |
|
N/A |
𝐼, 𝑉, 𝑋, 𝐿, 𝐶, 𝐷, 𝑀, 𝑉̅, 𝑋̅, 𝐿̅, 𝐶̅, 𝐷̅, 𝑀̅, etc | ||
|
Scientific Notation | |||
|
Residue Number System (RMS) - Complete Residue System - Reduced Residue System |