How to Convert Decimal to Binary (2026)

Every number you use daily is decimal — base 10, using digits 0–9. Binary is base 2, using only 0 and 1. Computers store and process everything in binary, so understanding the conversion is foundational for anyone working in programming, networking, or digital electronics.

The Division Method

To convert a decimal integer to binary, repeatedly divide by 2 and record the remainders. Read the remainders from bottom to top to get the binary result. For example, to convert 13: divide 13 by 2 to get 6 remainder 1, then 6 by 2 to get 3 remainder 0, then 3 by 2 to get 1 remainder 1, then 1 by 2 to get 0 remainder 1. Reading upward: 13 in binary is 1101. To verify, work back: 1×8 + 1×4 + 0×2 + 1×1 = 13.

Common Decimal to Binary Reference

For small numbers you will encounter often — especially powers of 2 and byte boundaries — it is worth recognising these on sight:

Converting Binary Back to Decimal

Going the other direction is straightforward. Each binary digit represents a power of 2, starting at 2⁰ on the right. Multiply each digit by its positional value and sum the results. For 10110: that is 1×16 + 0×8 + 1×4 + 1×2 + 0×1 = 22. A quick mental shortcut is to identify which powers of 2 have a 1-bit and add only those. With practice, you will recognise common patterns like 1111 (15) or 10000000 (128) without calculation.

Use the Decimal ↔ Binary Converter to do this instantly for any value, including large numbers and fractions.