Number Systems
A writing system for expressing numbers. Each number system defines a set of symbols that each represent a specific value.
Base (or radix)
Number of symbols defined by a number system.
Commonly used number systems
- Base 10 -
- Base 2 -
- Base 8 -
- Base 16 -
Conversion between number systems
10 —> n
Integer part
- Repeatedly divide the number (and the quotients) by
until reaching 1 - Write the remainders in reverse order
Fractional part
- Repeatedly multiply by
until fractional part reaches 0 - Write the integer parts in normal order
n —> 10
Multiply each digit by its positional value, and sum those values. Positional
value is
2 —> 8
- Split the given binary number into length 3 parts (prepend 0s if required)
- Convert each part to octal
- Join those together
2 —> 16
- Split the given binary number into length 4 parts (prepend 0s if required)
- Convert each part to hexagonal
- Join those together
16 —> 2
Convert each digit to 4-bit binary and join them together.
8 —> 2
Convert each digit to 3-bit binary and join them together.
8 <—> 16
Convert the number to base 2 or 10 and then conver to the target base.
Confusion about unit prefixes
In computing, the prefix kilo —just like other prefixes— has been used to
refer either
- Marketing of disk capacities (by disk manufacturers) - Memory capacities, and file sizes, disk capacities by operating systems
To avoid this confusion, 2 unit prefixes are used while measuring amounts of data.
- SI prefixes Defined by ISO. Based on powers of
. Examples: kilo, mega, giga. - Binary prefixes Defined by IEC. Based on powers of
. Examples: kibi, mebi, gibi.