Number Base Converter

The Number Base Converter transforms numeric values between any two positional numeral systems from base 2 through base 36, instantly and with the working shown. Programmers, electrical engineers, students, cryptographers, and embedded developers deal with multiple bases every day: binary (base 2) for raw bits and flags, octal (base 8) for Unix file permissions, decimal (base 10) for everyday math, and hexadecimal (base 16) for memory addresses, color codes, MAC addresses, hashes, and compact representations of bytes. Occasionally you also need base 32 or base 36 for short identifiers and custom encodings.

This tool converts in both directions simultaneously. Type a value in one base, watch every other common base update in real time. Toggle bit-level breakdown to see how each digit of a hex number maps to four binary bits, or how 755 in octal decomposes into the rwxr-xr-x permission bits. The converter also enforces validity — if you paste a hex string with a stray G character, the exact position of the error is highlighted. Fractional values are supported, so 0.5 decimal becomes 0.1 binary and 0.8 hexadecimal, with configurable precision for repeating expansions.

Positional numeral systems assign each digit a value equal to the digit itself multiplied by the base raised to the power of its position from the right. For an integer d_n d_(n-1) ... d_1 d_0 in base b, the decimal value is the sum of d_i times b^i for i from 0 to n. Converting to another base is the reverse: repeatedly divide the decimal value by the target base and read remainders from bottom to top.

This tool uses arbitrary-precision arithmetic (BigInt under the hood) so conversion works for numbers of any size — even 1024-bit cryptographic values. Standard JavaScript numbers would lose precision above 2^53, but BigInt keeps every bit exact. For integer conversion, the algorithm is O(n log b) where n is the digit count, which is effectively instant for any number you will paste into a browser.

Base 36 (digits 0-9 and a-z) is the largest base supported by convention because after 36 you run out of readable alphanumeric symbols without introducing case sensitivity or custom alphabets. Base 62 (0-9, A-Z, a-z case sensitive) and base 64 (standard MIME alphabet) exist but live outside classic number base tools — they belong to encoding tools for byte-oriented data.

Fractional conversion is trickier. The decimal 0.1 has no exact finite representation in binary (it is a repeating fraction, like 1/3 in decimal). The converter truncates or rounds to a configurable precision and marks the result as approximate when the expansion does not terminate. This matches how floating-point hardware represents the same values — useful for understanding why 0.1 + 0.2 ≠ 0.3 exactly in most programming languages.

Compared to a physical scientific calculator with a DEC/BIN/HEX/OCT mode, this browser tool shows every base simultaneously — you do not press a mode button and lose sight of the other representations. For teaching, debugging, and everyday conversion work, the all-at-once layout is faster and clearer.

Compared to Python parseInt or JavaScript Number.toString(radix), this tool does not require you to write code or worry about integer overflow. BigInt-backed arithmetic handles any size, and the step-by-step view is friendlier for learning how positional notation really works.

Compared to the Windows Calculator in programmer mode, this tool runs on any device in any browser. The programmer mode in Windows is good for quick bitwise operations (AND, OR, XOR, NOT, shifts) which this tool does not cover — for those, pair this converter with a dedicated bitwise operations tool.