Why Computers Use Number Systems
Human beings use a number system consisting of digits 0-9, corresponding to the number of fingers we have — this is called the decimal number system. Computers are digital devices and use only two states, either “0” or “1” (ON or OFF, True or False, High or Low). A computer understands the positional number system, where a small set of symbols (digits) represent different values depending on the position they occupy in the number.
Key Definitions
- Number system: a set of symbols and rules used to represent numbers in a certain base.
- Base (radix): the number of different symbols used in a given number system. The largest value a digit can have is always one less than the base (b-1).
- Binary digit (bit): made up of “0” or “1”. Computers deal with numbers in groups of bits, usually a power of 2 — 4 bits (a nibble), 8 bits (a byte), 16 bits (a half word), 32 bits (a word), or 64 bits (a double word).
Types of Number Systems
| Number System | Elements/Symbols |
|---|---|
| Binary (base 2) | 0, 1 |
| Octal (base 8) | 0, 1, 2, 3, 4, 5, 6, 7 |
| Decimal (base 10) | 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 |
| Hexadecimal (base 16) | 0-9, A=10, B=11, C=12, D=13, E=14, F=15 |
