About Binary to Decimal Converter
This converter turns a binary number (base 2) into a decimal number (base 10). It is free, needs no sign-up and runs in your browser, so nothing you enter is uploaded.
A binary number is written with the digits 0 and 1, and each place is worth a power of 2, counted from the right starting at 2^0. Multiply each digit by its place value and add the results.
Bit widths set the largest value: 8 bits reach 255, 16 bits reach 65535 and 32 bits reach 4294967295 when the number is unsigned. If the number is meant to be signed, turn on two's complement and choose the width.
The tool also accepts negative numbers, fractions (with the repeating block shown), numbers of any length and two’s complement for 8, 16, 32 or 64 bits.
How to use Binary to Decimal Converter
- Choose the Numbers mode to convert a value, or Text and ASCII to convert text.
- In Numbers mode, pick the base you are starting from, then type the number. Use a minus sign for negatives and a point for a fraction.
- Pick the target base. The result for binary, octal, decimal and hexadecimal appears together, with the target base and an extra base you can choose.
- Show steps is on by default. Turn on Group digits to split long results into blocks of 4 (binary and hex) or 3 digits.
- Turn on two’s complement and pick 8, 16, 32 or 64 bits to see how a signed whole number is stored.
- In Text mode, choose encode or decode and the base (2, 8, 10 or 16), then enter text or the bytes to decode.
Features
- Any base from 2 to 36, with results shown in binary, octal, decimal and hexadecimal together.
- Negative numbers and fractions, with a repeating block detected and shown in brackets, such as 0.0(0011) for 0.1.
- Step-by-step working for fractions by repeated multiplication, as well as for whole numbers.
- Big integers, with no 53-bit limit.
- Two’s complement for 8, 16, 32 and 64-bit signed integers.
- Step-by-step working for whole numbers: place values for the source base and repeated division for the target.
- Digit grouping in blocks of 4 or 3 for readable bit patterns.
- Text to and from UTF-8 bytes in bases 2, 8, 10 and 16.
- An ASCII table for codes 0 to 127 with decimal, hex, octal, binary and the character.
- Prefixes 0b, 0o and 0x accepted, and spaces, commas and underscores ignored.
- A copy button on each result.
Worked examples
10011100 (binary) gives 156 (decimal)
156 in decimal.
11111101000 (binary) gives 2024 (decimal)
2024 in decimal.
Place values in binary
| Place | Power | Value |
|---|---|---|
| 1 | 2^0 | 1 |
| 2 | 2^1 | 2 |
| 3 | 2^2 | 4 |
| 4 | 2^3 | 8 |
| 5 | 2^4 | 16 |
| 6 | 2^5 | 32 |
| 7 | 2^6 | 64 |
| 8 | 2^7 | 128 |
0 to 15 in binary, octal, decimal and hex
| Decimal | Binary | Octal | Hex |
|---|---|---|---|
| 0 | 0000 | 0 | 0 |
| 1 | 0001 | 1 | 1 |
| 2 | 0010 | 2 | 2 |
| 3 | 0011 | 3 | 3 |
| 4 | 0100 | 4 | 4 |
| 5 | 0101 | 5 | 5 |
| 6 | 0110 | 6 | 6 |
| 7 | 0111 | 7 | 7 |
| 8 | 1000 | 10 | 8 |
| 9 | 1001 | 11 | 9 |
| 10 | 1010 | 12 | A |
| 11 | 1011 | 13 | B |
| 12 | 1100 | 14 | C |
| 13 | 1101 | 15 | D |
| 14 | 1110 | 16 | E |
| 15 | 1111 | 17 | F |
Good to know
Worked example: 10011100 from binary to decimal
Decimal: 1 × 2^7 + 0 × 2^6 + 0 × 2^5 + 1 × 2^4 + 1 × 2^3 + 1 × 2^2 + 0 × 2^1 + 0 × 2^0 = 156
Worked example: 11111101000 from binary to decimal
Decimal: 1 × 2^10 + 1 × 2^9 + 1 × 2^8 + 1 × 2^7 + 1 × 2^6 + 1 × 2^5 + 0 × 2^4 + 1 × 2^3 + 0 × 2^2 + 0 × 2^1 + 0 × 2^0 = 2024
Privacy: how it works
- All conversions are done by code running in your browser tab. The numbers and text you enter are never sent to Ulkaa or anyone else.
- There is no account and no sign-up, and the tool costs nothing to use.
Tips
- Use Group digits to read long binary numbers: blocks of 4 line up with hex digits.
- Pick binary to hex when you want to read bits quickly: convert each group of four on its own.
- Use two’s complement with the width of your data type, for example 8 bits for a byte and 32 bits for a typical integer.
- If a result has a repeating block in brackets, the digits inside repeat forever, so a stored value is only an approximation of it.
Frequently asked questions
Is it really free?
Yes. There is no price, no trial and no credit card. Ulkaa Tool does the work with your own device, so there is no server bill to pass on to you.
Do I need an account?
No. There is no sign-up and no login. Open the page and use it. An Ulkaa account is not needed for anything on this tool.
Does it run in my browser?
Yes. Your numbers are processed by code running in your browser tab, on your own device.
Is my data uploaded?
No. Your numbers are never sent to Ulkaa or to anyone else. You can check this yourself by watching the Network tab in your browser developer tools while you use the tool.
How do I convert binary to decimal?
Multiply each digit by its place value (a power of 2) and add. For example, 10011100 is 156.
What is 11111101000 in decimal?
11111101000 in binary is 2024 in decimal.
What is the largest number 8 bits can hold?
Unsigned, 8 bits hold up to 11111111, which is 255. Signed (two's complement), they hold -128 to 127.
Which digits are valid in binary?
Binary uses the digits 0 and 1. Anything else is rejected with a message naming the digit.
More Number Base Converter pages
- Number Base ConverterConvert numbers between binary, octal, decimal, hexadecimal and any base from 2 to 36, or turn text into bytes.
- Decimal to Binary ConverterTurn a decimal number into binary, with the working shown.
- Binary to Hex ConverterTurn a binary number into hexadecimal, with the working shown.
- Hex to Binary ConverterTurn a hexadecimal number into binary, with the working shown.
- Decimal to Hex ConverterTurn a decimal number into hexadecimal, with the working shown.
- Hex to Decimal ConverterTurn a hexadecimal number into decimal, with the working shown.
- Decimal to Octal ConverterTurn a decimal number into octal, with the working shown.
- Octal to Decimal ConverterTurn an octal number into decimal, with the working shown.
- Binary to Octal ConverterTurn a binary number into octal, with the working shown.
- Octal to Binary ConverterTurn an octal number into binary, with the working shown.
- Hex to Octal ConverterTurn a hexadecimal number into octal, with the working shown.
- Octal to Hex ConverterTurn an octal number into hexadecimal, with the working shown.
- Binary to Text ConverterTurn binary bytes into text.