What is a numeral base?
A numeral base (radix) is how many digits are counted before a place value rolls over. Decimal (base 10) rolls over every 10, binary (base 2) every 2, hexadecimal (base 16) every 16. Computers work internally in binary since they only use 0 and 1, but long binary strings are hard to read, so hexadecimal — which packs 4 binary digits into one — is widely used in programming. Octal shows up in contexts like Unix file permissions.
How to convert between bases
Converting decimal to binary, octal, or hexadecimal
Divide repeatedly by the target base and read the remainders from bottom to top. For example, converting decimal 100 to binary: dividing by 2 repeatedly and stacking the remainders gives 1100100 (100 = 64 + 32 + 4).
Converting binary, octal, or hexadecimal to decimal
Multiply each digit by its place value (the base raised to a power) and sum the results. For example, binary 1100100 converts to decimal as 1×2⁶ + 1×2⁵ + 1×2² = 64 + 32 + 4 = 100.
Fast conversion between binary and octal/hexadecimal
Since 8 = 2³ and 16 = 2⁴, you can group binary digits into sets of 3 (octal) or 4 (hexadecimal) and convert each group directly, skipping decimal entirely. For example, grouping binary 1100100 into 4-digit chunks gives 0110 0100, which is hexadecimal 64.
What makes this tool different
- Converts base 2, 8, 10, 16, 32, and 64 simultaneously in real time — type into any one field and the rest update instantly
- Unlimited digits, thanks to BigInt-based arbitrary-precision arithmetic — accurate even beyond JavaScript's safe integer range
- Supports signed integers — enter a leading "-" for negative numbers
- Keyboard-friendly: ↑↓ to change by 1, Shift+↑↓ to change by 10
- Completely free, no sign-up, no ads
Frequently asked questions
How do I convert between number bases?
To convert from decimal, divide repeatedly by the target base and read off the remainders. To convert to decimal, multiply each digit by its place value and add them up. See "How to convert between bases" above for details.
Are base 32 and base 64 here the same as Base32/Base64 encoding?
No. This tool's base 32 and 64 are a simple positional numeral system that assigns digits in the order 0-9 → A-Z → a-z → +/ — it just represents a single integer in that base. It is not the same as RFC 4648 Base32/Base64 encoding, which encodes byte sequences into strings.
Can I convert numbers with a decimal point?
Currently only integers are supported; numbers with a fractional part are not.
Can I convert negative numbers?
Yes. Enter a leading "-" in any field and it will be treated as a signed integer and converted into the other bases accordingly.