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Binary to Decimal Converter

Convert binary numbers to base-10 (and back), one or many at a time — separate multiple values with a space. Looking to convert binary text instead of numbers? Use the Binary Translator.

Live conversion — results update as you type
How the math works

Powers of two, added up.

Every binary digit represents a power of 2. To convert by hand, line the digits up against 2⁷, 2⁶ ... 2⁰ and add up the columns where there's a 1.

2⁷2⁶2⁵2⁴2⁰
1286432168421
01110111

64+32+16+4+2+1 = 119, which is the decimal (and ASCII) value of the binary above.

Where this comes up

Common uses for a binary to decimal converter.

Binary-to-decimal conversion comes up in several real-world contexts, most of which involve reading data that was originally stored or transmitted in binary form.

Also known as: binary translator to decimal · base-2 to base-10 converter · binary number converter

FAQ

Binary to decimal, explained.

Does this handle negative numbers?
No — this tool converts unsigned (positive) binary values only. Signed binary (two's complement) needs an extra step beyond what's shown here.
I have a whole word or sentence in binary, not a single number — what do I use?
Use the Binary Translator instead, which decodes binary back into readable text rather than a numeric value.
How is this different from a normal calculator?
Most calculators don't have a dedicated base-2 mode by default. This tool skips the mode-switching and shows the powers-of-two math so you can also do it by hand.
What if I need hexadecimal instead of decimal?
See Binary to Hex — same binary input, hex output instead.