Number Base Converter

Bitwise operations

Both operands accept any base. Shifts treat B as a plain decimal bit count.

Why this converter never rounds

Every other number-base converter you have used probably breaks somewhere around 15 digits, and the reason is floating point. JavaScript numbers are IEEE 754 doubles, which hold exact integers only up to 2⁵³ − 1. Past that, 9007199254740993 and 9007199254740992 become the same value.

This tool converts through BigInt, which is arbitrary precision. A 256-bit hash, a 128-bit IPv6 address or a 300-digit number all convert exactly, in both directions. That is also why shift and mask results here stay correct for values far beyond what a 64-bit register could hold.

Base	Prefix	Digits	Typical use
2	0b	0 1	Bitmasks, flags, permissions
8	0o	0-7	Unix file modes such as 0644
10	none	0-9	Everything humans read
16	0x	0-9 a-f	Memory addresses, colours, hashes, byte dumps

Prefixes are accepted on any input. Typing 0x1F into the decimal field works and is interpreted as hexadecimal, which is handy when you are pasting values around quickly.

Two's complement, briefly

A bit pattern has no inherent sign. The byte 0xFF is 255 if you read it as unsigned, and −1 if you read it as a signed 8-bit integer. The rule: if the top bit of the chosen width is set, subtract 2^width from the unsigned value.

That is why the analysis panel reports signed interpretations at 8, 16, 32 and 64 bits separately rather than guessing one for you — the same 32-bit pattern legitimately means different things depending on the type you declared in your program.

What people actually use this for

• Permission bits. 0755 is not the number seven hundred and fifty-five. It is three octal digits: owner 7 (rwx), group 5 (r-x), others 5.
• Feature flags. One integer where each bit is a boolean. Test with flags & (1 << n), set with flags | (1 << n), clear with flags & ~(1 << n).
• Colour channels. 0x1A2B3C is three bytes: red 1A, green 2B, blue 3C. The byte breakdown below shows exactly that split.
• Network masks and subnets. A /24 is 0xFFFFFF00 as a 32-bit mask.

Frequently asked questions

Why does my decimal value come back slightly wrong elsewhere?

You have exceeded 2⁵³ − 1 and the other tool is using floating point. Values up to that limit are exact in a double; beyond it they are not.

Can I convert fractions such as 0.1?

No. This tool handles integers only, because positional conversion of fractional parts produces repeating expansions in most bases and is rarely what you want when working with bit patterns.

Why does a shift give a huge number?

Shifting left by n multiplies by 2ⁿ. With arbitrary precision there is no overflow, so 1 << 200 really is a 61-digit number rather than wrapping to zero.

What does "popcount" mean?

Population count: the number of bits set to 1. It is the standard way to answer "how many flags are enabled" on a bitmask and has a dedicated CPU instruction on most modern processors.