Free Number Base Converter

The Number Base Converter is a free online tool that converts numbers between binary, decimal, hexadecimal, and octal number systems.

Yes, it is completely free with no registration required. All conversions happen client-side in your browser.

The Number Base Converter supports binary (base 2), octal (base 8), decimal (base 10), and hexadecimal (base 16) conversions.

Absolutely. The Number Base Converter processes everything client-side in your browser. No data is uploaded to or stored on any server. Your content remains private on your device at all times.

Yes, the Number Base Converter is fully responsive and works on smartphones and tablets. You can use it on any device with a modern web browser -- no app download required.

No account or registration is needed. Simply open the Number Base Converter in your browser and start using it immediately. There are no sign-up walls or usage restrictions.

Simply enter your input in the provided field, adjust any settings to your preference, and the tool will process it instantly. You can then copy the result to your clipboard or download it.

The Number Base Converter works in all modern browsers including Chrome, Firefox, Safari, Edge, and Opera. For the best experience, use the latest version of your preferred browser.

The shortcut is that each hexadecimal digit maps to exactly four binary bits, so you convert one digit at a time instead of dividing the whole number. Write out the 4-bit pattern for each hex digit and join them: 0 is 0000, 9 is 1001, A is 1010, and F is 1111. For example, 0x2F becomes 0010 1111, and 0xFF becomes 1111 1111. This grouping is why a single byte is written as two hex digits and why programmers prefer hex over raw binary. Octal works the same way but in groups of three bits. If you want to skip the lookup table entirely, paste your hex value into the converter and it shows the binary, decimal, and octal forms at once, with an option to group the binary into 4- or 8-bit chunks for easy reading.

Two's complement is how computers store signed integers in a fixed number of bits. To represent a negative value, you invert every bit of the positive number and add one, which lets the same hardware add signed and unsigned numbers without special cases. The catch is that the result depends entirely on the word size: -1 is 11111111 in 8 bits but 11111111 11111111 in 16 bits, and the most significant bit acts as the sign. Each width also has a fixed range, such as -128 to 127 for 8-bit and -2,147,483,648 to 2,147,483,647 for 32-bit. This tool shows the two's complement at 8, 16, 32, and 64-bit word sizes, displays both the signed and unsigned reading of the same bits, and flags an overflow when a value will not fit the width you picked.

Computers store everything in binary, but long strings of ones and zeros are hard for people to read and easy to miscount, so hex and octal act as compact shorthand. The conversion is clean rather than arbitrary: each octal digit equals exactly three binary bits and each hex digit equals exactly four, so you can translate by grouping bits without doing any math. That is why a byte fits neatly into two hex digits, why a Unix permission like chmod 755 is written in octal, and why a CSS color such as #FF0000 is written in hex. One hex digit covers values 0 to 15, so it replaces four binary digits with a single character, cutting the length of the number by roughly three quarters. Paste a value into the converter to see all twelve supported bases side by side in one table.

Yes. The converter uses JavaScript's BigInt, which represents whole numbers of arbitrary size exactly, so every digit stays accurate no matter how many you enter. This avoids the rounding problem that affects ordinary floating-point math, where integers above 2 to the 53rd power can no longer all be represented and results silently lose precision. So you can convert a 64-bit register dump, a long hexadecimal hash, or a number far beyond what a standard calculator handles and trust that the binary, decimal, hex, and octal outputs are exact. The one exception is the IEEE 754 single-precision float view, which is intentionally an approximation because it shows how a value would be stored as a 32-bit float, not as an exact integer. For exact base conversion of huge integers, type or paste the value and read any base directly.

IEEE 754 single precision packs a number into 32 bits split into three parts: 1 sign bit, 8 exponent bits, and 23 mantissa (fraction) bits. The sign bit marks positive or negative, the exponent scales the value as a power of two, and the mantissa holds the significant digits, so the stored number is essentially a binary version of scientific notation. Because only 23 fraction bits are available, many everyday decimals cannot be represented exactly, which is why 0.1 plus 0.2 famously does not equal exactly 0.3 in most languages. This converter breaks a value into its sign, exponent, and mantissa bits and shows the raw hex bytes, so you can see precisely how the float is encoded. Enter a number in the float view to inspect each field and understand where rounding creeps in.