About decimal to binary converter
To convert decimal to binary, divide by 2 repeatedly and read the remainders from bottom to top. For example 13 gives 1101.
Worked example
Convert 75. 75 ÷ 2 = 37 remainder 1, 37 ÷ 2 = 18 remainder 1, 18 ÷ 2 = 9 remainder 0, 9 ÷ 2 = 4 remainder 1, 4 ÷ 2 = 2 remainder 0, 2 ÷ 2 = 1 remainder 0, 1 ÷ 2 = 0 remainder 1. Reading the remainders from last to first gives 1001011. Check: 64 + 8 + 2 + 1 = 75. A shortcut is to subtract the largest power of two that fits, repeatedly: 64, then 8, then 2, then 1.
How place values work
Each digit position is worth a power of the base. In decimal the places are 1, 10, 100, 1000 and so on. In binary they are 1, 2, 4, 8, 16, and in hexadecimal 1, 16, 256, 4096.
Why binary matters
- Computers store everything as binary; hexadecimal and octal are compact ways to write it.
- One hex digit equals exactly four binary digits, which is why programmers use it for colours, memory addresses and byte values.
- Octal groups three bits per digit and appears in Unix file permissions such as 755.
