Binary to Decimal Converter
This tool turns any binary number into its decimal value, and shows the position by position
math behind it, not just the final answer. Paste in a string of 0s and 1s and get the base 10 number
back straightaway, with the working available to expand if you want to check it.
How to convert binary to decimal
- Type or paste your binary number into the input box. Spaces between digits are fine and get ignored automatically.
- The tool reads each digit’s position, right to left, and works out its power of 2 value.
- Every digit’s value gets multiplied against its position and the results are added together.
- The total is your decimal number. Expand the working panel underneath to see every position and value that went into it.
How binary becomes decimal
Binary is a positional system, same idea as decimal, just with a different base. Each digit stands for a power of 2 instead of a power of 10, counting up from the right. To get the decimal value, multiply every digit by its position’s power of 2 and add the results. Here is binary 1011 worked out one digit at a time.
|
Position, power of 2 |
Digit |
Value contributed |
|---|---|---|
|
2 to the 3rd, 8 |
1 |
8 |
|
2 to the 2nd, 4 |
0 |
0 |
|
2 to the 1st, 2 |
1 |
2 |
|
2 to the 0th, 1 |
1 |
1 |
Adding the contributed values, 8 plus 0 plus 2 plus 1, comes to 11. So binary 1011 equals decimal 11. This same left to right logic scales to any length of binary number, the tool above just does it faster than doing it by hand.
The idea of writing every number with only two digits is older than computing itself. Gottfried Wilhelm Leibniz worked out a full binary numeral system using just 0 and 1, and submitted his paper on it to the French Academy of Sciences in 1703. It was printed in the Academy’s proceedings two years later, roughly two and a half centuries before the first electronic computer used the same base 2 logic to store and process numbers.
Two kinds of visitors land on this page
Students and anyone learning the method
Working through a binary to decimal homework problem by hand and wanting a fast way to check the answer, without a teacher having to grade the process.
Programmers and anyone reading raw data
Reading a binary value out of a register dump, a network trace, or a config file, and needing the base 10 number it actually represents without doing the math manually.
Decimal to Binary Converter and Binary Calculator
Binary Calculator
Add, subtract, multiply, and divide binary numbers directly, with a decimal cross check on the result.
Last updated September 2026. Every conversion here runs standard, checkable binary to ASCII logic. See the Binary Code Glossary for any term on this page you are not sure about.