Binary Converter: Decimal to Binary and Back

Binary Converter

Convert between decimal and binary numbers

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The decimal system (base 10) uses digits 0–9 and is what we use every day. The binary system (base 2) uses only digits 0 and 1, and is the language computers use internally.

For example, the binary number 1010 equals 10 in decimal (1×8 + 0×4 + 1×2 + 0×1). Type in either field below and the other updates instantly.

Decimal

Binary

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Quick Reference (all bases)

Binary is the fundamental language computers use internally, this converter switches between decimal and binary instantly in either direction.

How to use this binary converter

Enter a value in the Decimal field to see the equivalent in binary.
Or enter a value in the Binary field to see the equivalent in decimal, either field updates the other instantly.

What this converter does

The decimal system (base 10) uses digits 0-9 and is what we use every day. The binary system (base 2) uses only digits 0 and 1, and is the language computers use internally, since digital circuits naturally represent two states (on/off, high/low voltage).

1010 (binary) = 10 (decimal), since 1×8 + 0×4 + 1×2 + 0×1 = 10

Why computers use binary instead of decimal

Digital electronic circuits are built from switches that are most reliably represented as having exactly two states, on and off. Binary’s two digits (0 and 1) map directly onto this physical reality, which is why every layer of computing, from processor instructions to stored data, ultimately reduces to binary representation, even though humans typically interact with computers through decimal, text, or other higher-level representations.

Frequently asked questions

How do I convert binary to decimal?

Multiply each binary digit by its positional power of 2 (starting from the rightmost digit as 2⁰) and sum the results, for example, 1010 equals 1×8 + 0×4 + 1×2 + 0×1 = 10.

Why do computers use binary instead of decimal?

Digital circuits are most reliably built as two-state switches (on/off), which binary’s two digits (0 and 1) map onto directly, this is why binary underlies all digital computing at the hardware level.