Number Base Converter: Binary, Octal, Decimal and Hex
This number base converter changes a whole number from one base to another — binary, octal, decimal, hexadecimal or any base from 2 to 36. It shows the place-value working and the repeated division, and checks the answer by converting it back.
Result
Enter values and press Calculate to see the result.
Formula
Each digit is multiplied by the base raised to the power of its position, starting at 0 on the right.
To convert from decimal, divide by the new base again and again; the remainders, read from last to first, are the digits.
How to use this calculator
- Type the number. For hexadecimal, use the letters A–F (upper or lower case).
- Choose the base it is written in and the base you want.
- Press Calculate to see the converted number, its decimal value and the working.
Worked examples
255 in binary
Divide by 2 repeatedly: every remainder is 1, eight times.
Reading the remainders from bottom to top gives 11111111.
Binary 1011 to decimal
1 × 8 + 0 × 4 + 1 × 2 + 1 × 1 = 11.
255 in hexadecimal
255 ÷ 16 = 15 remainder 15, and 15 ÷ 16 = 0 remainder 15.
15 is the digit F, so 255 = FF.
Hexadecimal 1A3 to binary
1A3 = 1 × 256 + 10 × 16 + 3 = 419.
419 in binary is 110100011.
Common mistakes
- Reading the remainders from top to bottom; the first remainder is the last (rightmost) digit.
- Starting the place values at 1 instead of 0: the rightmost digit is multiplied by b⁰ = 1.
- Using digits that do not exist in the base, such as 2 in binary or G in hexadecimal.
Frequently asked questions
How do you convert decimal to binary?
Divide by 2 and write down the remainder; repeat with the quotient until it is 0. Read the remainders from the last to the first. 13 → 1101.
How do you convert binary to decimal?
Multiply each digit by its place value (1, 2, 4, 8, … from the right) and add: 1011 = 8 + 0 + 2 + 1 = 11.
What are the letters in hexadecimal?
Hexadecimal needs 16 digits, so A–F stand for 10–15. FF = 15 × 16 + 15 = 255.