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Binary to Decimal Converter

Convert binary to decimal and back, and see exactly how place value turns a string of 0s and 1s into a number.

Binary to Decimal Converter

Editing either field updates the other. Binary accepts only 0 and 1; spaces are ignored.

🔒 Nothing you enter is sent anywhere or stored. All processing happens in your browser.

How it works

Binary (base 2) is the language computers use internally: every value is a string of 0s and 1s, where each position is worth twice the one to its right. Decimal (base 10) is how people usually write numbers. This converter moves between the two in both directions at once.

Type a binary string in the left field and its decimal value appears on the right; type a decimal number on the right and its binary form appears on the left. Because the two fields are linked, you never have to press a button — just edit whichever side you have and read the other. Spaces inside binary are ignored so you can group bits into nibbles or bytes for readability.

Only valid input is accepted: binary must be made of 0s and 1s, and decimal must be a whole, non-negative number. Anything else shows an error rather than producing a misleading result, and the maths uses arbitrary precision so even very long bit strings convert exactly.

Examples

Binary 1010 → decimal 10.
Decimal 255 → binary 11111111 (one full byte).
Binary 1000 0000 (spaces ignored) → decimal 128.
Binary 1002 → error, because 2 is not a binary digit.

Binary place value & chart

Reading right to left, each position is worth double the one before it:

Position (from right)87654321
Place value1286432168421

Binary chart (0–16)

DecimalBinaryDecimalBinary
0091001
11101010
210111011
311121100
4100131101
5101141110
6110151111
71111610000
8100025511111111

Common milestones: 8 bits (one byte) hold 0–255, and each extra bit doubles the range. That's why you see 256, 1024, and 65536 everywhere in computing.

Frequently asked questions

Do I need to press convert?
No. The two fields are linked, so editing either one updates the other automatically as you type.
Can I use spaces to group bits?
Yes. Spaces in the binary field are ignored, so you can write bytes like 0100 0001 for readability.
Does it support negative numbers?
No. It works with non-negative whole numbers. Signed binary uses conventions like two's complement, which are outside this tool's scope.
How large can the numbers be?
Very large. Conversion uses arbitrary-precision integers, so long binary strings convert without rounding errors.
Is my data uploaded?
No. Everything is computed locally in your browser and nothing is sent anywhere.
How do you convert binary to decimal?
Each binary digit represents a power of two, doubling from right to left (1, 2, 4, 8, 16…). Add the place values wherever there's a 1. For example 1010 = 8 + 0 + 2 + 0 = 10. This tool does it instantly, and the chart below shows the pattern.
How do you convert decimal to binary?
Repeatedly divide the number by 2 and record the remainders, then read them bottom to top. 10 ÷ 2 = 5 r0, 5 ÷ 2 = 2 r1, 2 ÷ 2 = 1 r0, 1 ÷ 2 = 0 r1 → 1010. Switch this tool to the other direction to do it automatically.
What is 1111 in decimal?
1111 in binary is 8 + 4 + 2 + 1 = 15. In general, n ones in a row equal 2ⁿ − 1, so four ones make 15 and eight ones (11111111) make 255 — the largest value in a single byte.
Why do computers use binary?
Digital circuits have two stable states — on and off — which map naturally to 1 and 0. Building everything from two states is simpler and more reliable than using ten, so binary underpins all digital computing.
Is my input uploaded?
No — the conversion runs entirely in your browser.