Binary and Hexadecimal Explained: Converting Number Bases

Every number system uses place value. In decimal each place is a power of 10; in binary each place is a power of 2 and the only digits are 0 and 1; in hexadecimal each place is a power of 16, with digits 0–9 and A–F. Convert to decimal by multiplying out place values, and from decimal by repeated division.

Place value in binary

$101101_2$ means

Decimal to binary: repeated division

Divide by 2 repeatedly and write down the remainders, then read them bottom to top.

$13 \div 2 = 6$ r 1, $6 \div 2 = 3$ r 0, $3 \div 2 = 1$ r 1, $1 \div 2 = 0$ r 1, so $13 = 1101_2$.

For a bigger example, $2026 = 11111101010_2$.

Hexadecimal

Hex digits: 0–9 then A = 10, B = 11, C = 12, D = 13, E = 14, F = 15.

$FF_{16} = 15 \times 16 + 15 = 255$, the largest value in one byte.

Binary ↔ hex shortcut

Each hex digit is exactly four binary digits. Group binary digits in fours from the right:

$101101 = 0010\;1101 = 2\,D$, so $101101_2 = 2D_{16}$.

Common mistakes

• Reading the division remainders top to bottom instead of bottom to top.
• Forgetting that A–F stand for 10–15.
• Grouping binary digits from the left instead of the right.

Practice questions

1. Convert $10011_2$ to decimal.
2. Convert 37 to binary.
3. Convert $1F_{16}$ to decimal.

Answers: 1) 19 2) $100101_2$ 3) 31

Convert between any bases from 2 to 36 with the binary converter, which shows both methods. Powers of 2 come from the exponents calculator, and division with remainders from the remainder calculator.

Frequently asked questions

Open the calculator →