How Decimal to Binary Conversion Works

Decimal (base-10) numbers are converted to binary (base-2) by repeatedly dividing the number by 2 and recording the remainder. The binary equivalent is the sequence of remainders read in reverse order.

For example, converting 42 to binary:

42 ÷ 2 = 21 remainder 0
21 ÷ 2 = 10 remainder 1
10 ÷ 2 = 5 remainder 0
5 ÷ 2 = 2 remainder 1
2 ÷ 2 = 1 remainder 0
1 ÷ 2 = 0 remainder 1

Reading the remainders from bottom to top gives the binary equivalent: 101010