Number Base Converter

A positional number system in base N uses N distinct digits and gives each position a weight of N^k. The number 255 in base 10 = 2×100 + 5×10 + 5×1. The same value in base 16 is FF = 15×16 + 15×1. The "digits" 0–9 are reused for bases ≤10; bases 11–16 add A–F; bases 17–36 continue through Z. Above 36, conventions diverge — Base58, Base62, and Base64 each have their own non-positional alphabets.

Base 2 is the only one where every digit is one bit. Base 8 groups bits in threes (one octal digit = 3 bits), base 16 groups in fours (one hex digit = 4 bits). This is why hex is preferred over octal for byte-aligned data — each byte is exactly two hex digits, no padding alignment math required.

• Base 32 — used in Crockford Base32 (case-insensitive, no I/L/O/U to avoid confusion) for human-typeable IDs. Different from RFC 4648 Base32 — same alphabet length, different ordering, different padding.
• Base 36 — alphanumeric 0-9 a-z. JavaScript Number.prototype.toString(36) produces it natively. Useful for short, URL-safe, human-readable IDs when collisions can be tolerated.
• Base 58 — Bitcoin-style; removes 0, O, I, l. Not a positional base in the textbook sense — it is technically arithmetic-style but encoded against a custom alphabet.
• Base 64 — not a positional base, it is a binary-to-text encoding. Three bytes in, four characters out. Do not confuse with "base 64 numbers" — those would need 64 digit symbols and the alphabet is not for arithmetic.

• You are reading a register dump and need to see what bits are set in 0xDEADBEEF — paste the hex, see the 32-bit binary, count the ones.
• You are debugging a Unix file permission and need to confirm that 0o644 really is rw-r--r-- before chmod-ing in production.
• You inherited code that stores feature flags as a decimal bitfield (37 = 0010 0101 = flags 0, 2, 5) and need to figure out which features are enabled.
• You are interviewing a candidate and want a concrete "convert 0xCAFE to base 8" exercise that exercises division-with-remainder thinking.

• It will not convert negative numbers in two's complement representation. -1 in binary is "negative one"; whether it is shown as -1 or as ...11111111 depends on the bit width you assume. Use a dedicated two's-complement viewer for hardware debugging.
• It will not handle fractional bases. 0.1₁₀ ≠ 0.1₂ — there is no terminating binary representation of decimal 0.1. For floating-point bit inspection use an IEEE 754 visualizer instead of base conversion.
• It will not parse "0x" / "0b" prefixes automatically in every field — pick the input base explicitly so the tool does not silently treat your hex as decimal.