Definition
Put definition of generic base n
Popular Bases
Binary
Binary, or base 2, is the most commonly used number system in computers. The base 2 system only uses the digits, 0 and 1. Each digit in binary represents an extra power of two starting from the rightmost digit. For example the binary number 1101 can be expressed as (1*23) + (1*22) + (0*21) + (1*20).
Converting from Decimal to Binary
The fastest and most efficient way to convert from decimal to binary is by dividing by 2 and keeping track of the remainder. We stop when the quotient = 0. Then read the numbers stating from the bottom to get the binary number.
For example, to convert 156 from decimal to binary we do:
156 | / 2 = | 78 | r = | 0 |
78 | / 2 = | 39 | r = | 0 |
39 | / 2 = | 19 | r = | 1 |
19 | / 2 = | 9 | r = | 1 |
9 | / 2 = | 4 | r = | 1 |
4 | / 2 = | 2 | r = | 0 |
2 | / 2 = | 1 | r = | 0 |
1 | / 2 = | 0 | r = | 1 |
Thus by reading the numbers starting from the bottom we get, 10011100
Hexadecimal
Hexadecimal or base 16 is commonly used because of the less space it takes up. A hexadecimal number consists of the digits 0-9 and A-F to represent the values 10-15. This works in the same way as binary but instead of incrementing in powers of 2 it increments in powers of 16.
Example
The hexadecimal number A5B can be represented as (10*162) + (5*161) + (11*160) which is 2651 in decimal.
Converting from Binary to Hexadecimal
You can group 4 digits in binary as 1 digit in hexadecimal because 16 is 2^^4.
Example
To convert 100111000100 to hexadecimal we group in fours starting from the right to convert to hexadecimal.