Decimal to Binary Conversion

To convert decimal to binary, repeatedly divide by 2 and track the remainders. The remainders, read in reverse, give you the binary representation.

Example: Convert $13_{10}$ to binary. $13 \div 2 = 6$ remainder $1$. $6 \div 2 = 3$ remainder $0$. $3 \div 2 = 1$ remainder $1$. $1 \div 2 = 0$ remainder $1$. Reading remainders bottom-up: $1101_2$.

Why does this work? Each division by 2 extracts the least significant bit (rightmost digit). Dividing again extracts the next bit. You are peeling off bits from right to left, which is why you reverse the remainders.