Base (radix) is the number of unique digits and letters to represent a number. The number bases are mostly up to 36 as there are 10 digits (0 to 9) and 26 English alphabet letters (A to Z) but there can be many more number bases if more letters and symbols are included.
The most common base is the decimal (base-10) base that only uses digits from 0 to 9. We use decimal numbers in daily life to represent any number. The binary (base-2), octal (base-8) and hexadecimal (base-16) are mostly used in computing.
How are base numbers converted?
To convert a base number to another base number, although there are some direct conversion methods between binary, octal and hex numbers, usually you have to convert the base number into a decimal number first and then convert that decimal number into the other base number.
To convert from a decimal number to another base number:
To convert a decimal number into another base number, the decimal number is divided repeatedly by the new base number and the remainder is taken until the quotient becomes zero. The first remainer will be the least significant digit (rightmost digit) and the last remainder will be the most significant digit (leftmost digit).
For example, these are the steps to convert the decimal number "50" to base 6:
1) 50 / 6
2) Quotient (8), Remainder (2)
3) 8 / 6
4) Quotient(1), Remainder (2)
5) 1 / 8
6) Quotient(0), Remainder (1)
7) Reverse the remainders from least to most significant digits 1, 2, 2
that makes decimal 50 is equal to 122 in base 6.
To convert a base number to a decimal number:
To convert a base number to the equivalent decimal number, multiply the base number digit by the power of the base numbers digit location and sum all the multipliers. The power starts from 0 and increases by one as you go left by each base number digit.
For example, these are the steps to convert base 6 number "122" to decimal:
1) (1 * 62) + (2 * 61) + (2 * 60)
2) 36 + 12 + 2
that makes base 6 number 122 is equal to 50 in decimal form.
To convert a base number to another base number:
To convert a base number to another base number, convert the base number to decimal number first then convert the decimal number to the new base number.
There are some shortcuts to convert between binary, octal and hex numbers. For those, please visit the related converters listed below for the steps.