Binary to Decimal Converter
Type a binary number of any length to see it in decimal, with every step of the working.
Binary to decimal table
| Binary | Decimal |
|---|---|
| 0 | 0 |
| 1 | 1 |
| 10 | 2 |
| 11 | 3 |
| 100 | 4 |
| 101 | 5 |
| 111 | 7 |
| 1000 | 8 |
| 1010 | 10 |
| 1111 | 15 |
| 10000 | 16 |
| 100000 | 32 |
| 1000000 | 64 |
| 1100100 | 100 |
| 1111111 | 127 |
| 10000000 | 128 |
| 11111111 | 255 |
| 100000000 | 256 |
| 1111101000 | 1000 |
| 10000000000 | 1024 |
Worked examples
10 in decimal
1010 (binary)
10 (decimal)
Decimal value 10.
255 in decimal
11111111 (binary)
255 (decimal)
Decimal value 255.
2026 in decimal
11111101010 (binary)
2026 (decimal)
Decimal value 2026.
About Binary to Decimal Converter
This converter turns binary numbers into decimal and shows how. To convert binary to decimal, multiply each binary digit by its place value, which is a power of 2, and add the results. For example, 1010 in binary is 10 in decimal, and 11111101010 is 2026.
Binary is the language of computers: every value in memory is a pattern of bits, each one a 0 or a 1. Decimal is the base 10 system we count in every day, with place values of ones, tens, hundreds and so on. Numbers of any length are converted exactly, because the tool works with whole numbers digit by digit instead of rounding.
How to use Binary to Decimal Converter
- Type or paste a binary number into the first box. Spaces, underscores and prefixes such as 0x are ignored.
- Read the decimal result straight away in the second box, grouped for easier reading if you leave the box ticked.
- Look at the working table to see each step of the method.
- Copy the result, or use the swap button to convert decimal back to binary.
Common uses
- Reading or setting bit flags and permissions in software
- Working out subnet masks and IP address ranges
- Computer science and GCSE or A level homework
- Checking how a number is stored in memory
Frequently asked questions
How do I convert binary to decimal by hand?
Multiply each binary digit by its place value, which is a power of 2, and add the results. The working table on this page shows exactly these steps for the number you type.
What is 11111111 in decimal?
11111111 in binary is 255 in decimal. In decimal it is 255, the largest number that fits in one byte.
What is 11111101010 in decimal?
11111101010 in binary is 2026 in decimal.
Can it convert very large numbers?
Yes. Whole numbers with up to 4,096 digits are converted exactly. The working table shows the first rows when a number is very long.
Does it handle fractions or negative numbers?
Negative whole numbers are converted with their minus sign kept. Fractions are not supported, because many fractions that end in one base repeat for ever in another.