Number Base Converter

About Number Base Converter

Any number can be represented in any base (2-36). Common bases: binary (2), octal (8), decimal (10), hexadecimal (16).

How to use this calculator

1. Enter the number you want to convert in its current base.
2. Choose the starting base, then choose the target base.
3. Check the converted result in the new base.
4. Use the step-by-step explanation to see how the digits were transformed.

The formula explained

The notation \(n_{base1} \rightarrow n_{base2}\) means a number written in one base is rewritten in another base without changing its value. The calculator finds the same quantity, just expressed with a different place-value system.

• n = the number being converted
• base1 = the original base the number is written in
• base2 = the base you want the number converted to

Step by step method

1. Convert the original number to base 10 by expanding it with place values.
2. Convert the base 10 value into the target base by repeated division or place-value grouping.
3. Write the remainders in reverse order to form the new number.

Worked example

Problem. Convert \(1011_2\) to base 10.

1. Start with place values: \(1011_2 = 1\cdot2^3 + 0\cdot2^2 + 1\cdot2^1 + 1\cdot2^0\).
2. Calculate each term: \(1\cdot8 + 0\cdot4 + 1\cdot2 + 1\cdot1 = 8 + 0 + 2 + 1\).
3. Add them: \(11\). So \(1011_2 = 11_{10}\).

Tips and common mistakes

• Make sure every digit is valid for the chosen base, for example, a base 2 number can only use 0 and 1.
• If you are converting from a larger base to a smaller one, do not change the value digit by digit, first rewrite it using place values.

Frequently asked questions