Number Base Converter

2026-10-17

Convert a whole number between decimal, binary, hexadecimal and octal at 8, 16, 32 or 64 bits, read the same bits as unsigned or as signed two's complement, flip single bits in a bit grid, and decode or build bitmasks from bit flags you name yourself.

How to use the number base converter

1. Pick the bit width: 8, 16, 32 or 64 bits, the size of your integer (one byte is 8 bits).
2. Type a whole number into any of the four fields. The other three update as you type. Spaces, underscores and the prefixes 0x, 0b and 0o are allowed. In the decimal field you can also write a power of two such as 2^63 or 2^32-1.
3. Choose whether the decimal field shows the unsigned or the signed (two's complement) value. The result box always lists both readings.
4. Flip single bits in the bit grid. The table under it lists every bit that is 1 with its weight 2ⁿ and its hex mask.
5. In the bit flags section, pick or write a set of names, then decode a value or tick names to build one.

How it works

Every base uses positional notation. A number written in base b with the digits dk … d1 d0 has the value

value = d_k × b^k + … + d₁ × b + d₀

Here b is the base (2, 8, 10 or 16), di is the digit in position i counted from the right starting at 0, and every digit is smaller than the base. Hexadecimal needs six extra digits, so A to F stand for 10 to 15. By hand, you convert a decimal number by dividing it by the base repeatedly and reading the remainders from last to first.

Hex and octal are shorthand for binary. Because 16 = 2⁴, one hex digit is exactly four bits (a nibble), and because 8 = 2³, one octal digit is exactly three bits. That is why the bit grid shows a hex digit for every group of four bits.

The tool stores the number as a pattern of exactly n bits, where n is the width, and calculates with arbitrary-precision integers, so 64-bit values stay exact. The same pattern p has two readings:

unsigned = p
signed = p − 2ⁿ if bit n−1 is 1, otherwise signed = p

An n-bit unsigned number runs from 0 to 2ⁿ − 1, a signed one from −2ⁿ⁻¹ to 2ⁿ⁻¹ − 1. A negative decimal input is stored as p = value + 2n. If you switch to a smaller width and the number no longer fits, only the lowest n bits are kept and a note says so.

Examples

Example 1 – 255 at 8 bits. 255 ÷ 16 = 15 remainder 15, and 15 ÷ 16 = 0 remainder 15, so the hex digits are F and F: 0xFF. In binary that is 0b11111111, and in octal 3 × 64 + 7 × 8 + 7 = 255 gives 0o377. The top bit is 1, so the signed reading is 255 − 256 = −1.

Example 2 – −1 at 16 bits. Choose 16-bit and Signed, then type −1. The stored pattern is −1 + 65,536 = 65,535, which is 0xFFFF: sixteen ones, octal 0o177777. It also works the other way: type FFFF in the hex field and the decimal field shows −1 (or 65,535 in Unsigned mode).

Example 3 – 2⁶³ at 64 bits. Type 2^63 or 9223372036854775808. The hex field shows 8000 0000 0000 0000, binary is a 1 followed by 63 zeros, and octal is a 1 followed by 21 zeros, because 2⁶³ = 8²¹. Only bit 63 is set, so the signed reading is 2⁶³ − 2⁶⁴ = −9,223,372,036,854,775,808, the smallest 64-bit signed integer.

Example 4 – decoding flags. In the set “User permissions”, bit 0 is CAN_READ and bit 3 is IS_ADMIN. A user with both has the value 2⁰ + 2³ = 1 + 8 = 9, binary 1001, hex 0x0009 at 16 bits. Typing 9 into “Value to decode” shows CAN_READ | IS_ADMIN. In the file permission set, octal 0o755 = 7 × 64 + 5 × 8 + 5 = 493 decodes to seven names, from OTHERS_EXECUTE (bit 0) up to OWNER_READ (bit 8), because each octal digit is one read-write-execute group.

Signed and unsigned: the same bits, two readings

The bits never say whether they are signed. The program that reads them decides. At 8 bits:

Common mistakes come from forgetting the width. 0xFF is −1 as a signed byte but 255 as a signed 16-bit number, because there it is 0x00FF and its top bit is 0. When a signed value moves to a wider type it is sign-extended: −1 at 8 bits (0xFF) becomes 0xFFFF at 16 bits, which is what the converter does when you widen in Signed mode.

Bit flags and bitmasks

A bit flag is a yes/no setting stored in one bit, so a single integer can hold up to 64 of them. The mask of flag number n is 1 << n, which equals 2ⁿ. Four bitwise operations cover almost everything you do with flags:

• Set: value | mask turns the flag on.
• Test: (value & mask) != 0 is true when the flag is on.
• Clear: value & ~mask turns it off.
• Toggle: value ^ mask flips it.

Export a set as JSON or text to keep or share it, and import it later. The JSON format is {"name": "…", "flags": [{"bit": 0, "name": "CAN_READ"}]}; a plain object such as {"0": "CAN_READ", "3": "IS_ADMIN"} is also accepted. A line with more than one bit, such as BOTH = 0x03, is skipped with a message, because a flag needs exactly one bit.

Frequently asked questions

Why does the hex value have leading zeros?

With “Leading zeros” ticked, binary and hex are padded to the full width, so you see all 16, 32 or 64 bits of the pattern. Untick it to show 0x1ED instead of 0x01ED. The value is the same.

What do 0x, 0b and 0o mean?

They are prefixes many programming languages use to mark hexadecimal, binary and octal literals. Older C-style code marks octal with a plain leading zero instead, so 0755 there means octal 755. This converter reads a plain leading zero in the decimal field as decimal.

Why is 0xFFFF sometimes −1 and sometimes 65,535?

Both are correct readings of the same sixteen ones. Unsigned it is 65,535; in two's complement the top bit counts as −32,768, which gives −1. The result box always shows both.

Can I convert fractions or numbers longer than 64 bits?

No. This tool handles whole numbers up to 64 bits. For binary fractions such as 0.1, and for widths other than 8, 16, 32 or 64, use the Two's Complement Calculator.

How do I enter a negative number?

Type it with a minus sign in the decimal field. Hex, binary and octal fields take a bit pattern, so for −1 at 16 bits you type FFFF there.

Is anything I type sent to a server?

No. All conversions run in your browser. Your numbers, settings and flag sets are stored only in this browser's local storage, and nothing is uploaded or shared.

Related tools

• Two's Complement Calculator – any width from 2 to 64 bits, binary addition with overflow, and fractions.
• Subnet Calculator – IPv4 network, broadcast and host range, with the mask in binary.
• Truth Table Generator – truth tables for logical expressions.
• Boolean Algebra Simplifier – the minimal sum-of-products and product-of-sums form of a Boolean expression.
• Logic Gate Simulator – build circuits from logic gates and watch the outputs change.
• Number systems (Číselné sústavy) – a school lesson on number bases, in Slovak.