Number Base Converter
A positional numeral system represents numbers using a fixed set of digits and assigns values based on the position (place value) of each digit. This converter handles the four bases used most commonly in computing and mathematics: binary (base 2), octal (base 8), decimal (base 10), and hexadecimal (base 16). Enter a number in any base and the tool converts it to all four simultaneously. The method converts to decimal first (by summing digit times base to the power of position) and then from decimal to each target base using repeated division.
Base conversion method
Decimal value = sum of (digit * base^position) for each digit
Then convert decimal to target base by repeated division
To convert from any base to decimal, multiply each digit by the base raised to its positional power and sum the results. Then convert the decimal integer to any other base by dividing by the target base repeatedly and collecting remainders.
Quick reference table
- Binary 1111 = Octal 17 = Decimal 15 = Hex F
- Binary 1000 0000 = Octal 200 = Decimal 128 = Hex 80
- Binary 1111 1111 = Octal 377 = Decimal 255 = Hex FF
- Decimal 1,024 = Hex 400 = Binary 100 0000 0000
- Hex FF = 15*16 + 15 = 255 in decimal; hex is compact for byte values.
Number base converter: frequently asked questions
What is a number base?
A number base (or radix) defines how many distinct digits a positional numeral system uses. Base 10 (decimal) uses digits 0-9. Base 2 (binary) uses only 0 and 1. Base 8 (octal) uses 0-7. Base 16 (hexadecimal) uses 0-9 and A-F.
How do you convert decimal to binary?
Divide the decimal number by 2 and record the remainder (0 or 1). Divide the quotient by 2 again, recording the remainder. Continue until the quotient is 0. Read the remainders from bottom to top to get the binary representation. For example, 13 = 1101 in binary.
Why is hexadecimal used in computing?
Hexadecimal is a compact way to represent binary data. Each hexadecimal digit represents exactly 4 binary bits (a nibble), so a byte (8 bits) is always two hex digits. Colors in web design (e.g., #FF5733) and memory addresses use hex for readability.
What are the letters A-F in hexadecimal?
Hexadecimal needs 16 distinct digits. After 0-9, the letters A through F represent decimal values 10 through 15. So hex A = decimal 10, B = 11, C = 12, D = 13, E = 14, F = 15.
How do you convert between bases without going through decimal?
Binary and octal (base 8 = 2^3) or binary and hex (base 16 = 2^4) can be converted directly by grouping bits. To convert binary to hex, group bits in fours from the right and replace each group with its hex digit. To convert binary to octal, group in threes.
Official sources
- NIST SP 800-57 Part 1, Key Management (covers binary representation in cryptography): csrc.nist.gov.
- IEEE 754-2019 Standard for Floating-Point Arithmetic: standards.ieee.org.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.