How to Convert Decimal to Binary (Step by Step)

The divide-by-2 method

To convert a decimal number to binary, repeatedly divide by 2 and record the remainder (0 or 1) each time. When the quotient reaches 0, read the remainders from bottom to top — that sequence is the binary number.

A worked example

Take 13: 13 ÷ 2 = 6 remainder 1; 6 ÷ 2 = 3 r 0; 3 ÷ 2 = 1 r 1; 1 ÷ 2 = 0 r 1. Reading the remainders bottom-to-top gives 1101, so 13 in binary is 1101.

Checking with place values

You can verify by adding place values. From the right, binary positions are worth 1, 2, 4, 8, 16… For 1101 that’s 8 + 4 + 0 + 1 = 13. A decimal-to-binary converter does the whole process instantly for any number.

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