How does a binary number become decimal?

Each bit is multiplied by a power of two from right to left and the results are summed, so 101010 equals 32 + 8 + 2 = 42.

Can I convert decimal numbers to binary too?

Yes. Select Decimal to Binary, enter one or more decimal whole numbers, and the converter returns exact binary values in the same order.

Can I paste binary with spaces between groups?

Yes. Spaces and underscores inside a value are ignored, so 1010 1010 and 10101010 convert to the same decimal number.

Will very long bit strings lose precision?

No. Conversion uses arbitrary-precision integers, so bit strings longer than 64 bits convert exactly instead of rounding.

Decimal to Binary and Binary to Decimal Conversion

Convert decimal numbers to binary or binary numbers to decimal instantly. Switch directions and paste one value per line for batch conversion. Decimal input supports negative whole numbers, while binary input accepts 0b prefixes, spaces, and underscores. Values of any length are converted with exact arbitrary-precision math locally in your browser.

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Decimal to Binary and Binary to Decimal Conversion

Decimal numbers (one per line)

Binary output

Popular Number Base Converter

About Decimal to Binary and Binary to Decimal Conversion

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Decimal numbers (one per line)

Binary output