Hex Converter

About Hex Converter

Type a value in hexadecimal, decimal, or binary and the tool shows the other two. It uses JavaScript's BigInt under the hood, so there is no length limit: a 64-bit hash or a 128-bit UUID written as one number converts without its last digits being rounded away.

With the default bit width (Unlimited) values are unsigned, so FF means 255. Yet in a debugger or a hex dump, FF very often means -1. Pick a bit width of 8, 16, 32 or 64 and turn on Signed (two's complement), and FF reads as -1 and the decimal field accepts negative numbers such as -5. The sections below explain why the same bit pattern can be both. Fractions are not accepted in any mode.

Why 0xFF can be -1: two's complement

Memory does not store a sign separately. An 8-bit cell simply holds 11111111; read it as an unsigned byte (uint8) and you get 255, read it as a signed byte (int8) and you get -1. Practically every modern CPU represents signed integers in two's complement, and the rule is short: in an n-bit value, if the top bit is 1, the real value is the unsigned value minus 2^n.

For 8 bits, 0xFF = 255 - 256 = -1, 0x80 = 128 - 256 = -128, and 0x7F = 127. That is why int8 runs from -128 to 127, one step longer on the negative side. Going the other way, to write -5 as an 8-bit hex value, set the width to 8, turn on signed mode and enter -5 in decimal (in unsigned mode, entering 256 - 5 = 251 gives the same): you get FB, or 11111011 in binary.

Two's complement won because one adder circuit handles both addition and subtraction. Add 00000001 to 11111111 (-1) and you get 1_00000000; the carry falls off the end of the 8-bit cell and what remains is 0. Sign-magnitude and ones' complement schemes both end up with a +0 and a -0; two's complement has exactly one zero.

You cannot read a sign without the bit width

Whether FF is -1 depends entirely on how wide the container was. In a 16-bit field, 0x00FF is just 255, and -1 is 0xFFFF. In 32 bits it is 0xFFFFFFFF; in 64 bits, sixteen F's. What matters is not how many F's you see but whether the top bit of the full width is set.

With the width set to Unlimited the tool strips leading zeros, so entering 0x00FF returns FF. Pick a width and the output is zero-padded to it (FF becomes 00FF at 16 bits), and values that do not fit are flagged as out of range.

• 8-bit (byte): 00 to FF; signed range -128 to 127
• 16-bit (short): 0000 to FFFF; signed range -32,768 to 32,767
• 32-bit (int): largest signed value 0x7FFFFFFF = 2,147,483,647
• 64-bit (long): largest signed value 0x7FFFFFFFFFFFFFFF = 9,223,372,036,854,775,807

Why programmers write hex at all

Since 16 = 2^4, one hex digit maps to exactly four binary digits (a nibble). A byte is always two hex digits, and you can convert in your head by splitting binary into groups of four. Decimal has no such alignment: the jump from 255 to 256 changes the digit count for reasons unrelated to bit boundaries. That is why color codes (#RRGGBB), MAC addresses, memory addresses and UTF-8 byte sequences are all written in hex.

The 0x prefix from C-family languages and the 0b prefix for binary are both accepted here. Spaces are ignored, so a byte-spaced value like DE AD BE EF can be pasted as is. Input is case-insensitive; hex output is uppercase.

Common traps when reading hex from other tools

Byte order. A hex dump of a 32-bit integer on an x86 or ARM machine usually shows bytes in little-endian order, so the value 0x12345678 appears in memory as 78 56 34 12. If you paste the dump bytes in that order, you will get 0x78563412 = 2018915346 instead of 305419896. Reverse the bytes first.

Sign extension. When a signed byte like 0xFB (-5) is widened to 32 bits, the CPU copies the top bit into all new positions and you get 0xFFFFFFFB, not 0x000000FB. Seeing a run of leading F's in a register usually means a small negative number was sign-extended.

Worked examples

How to use it

1. Pick the field for the base you have: hex, decimal or binary.
2. Enter the value; 0x/0b prefixes and spaces are fine. To read it as a signed integer, pick a bit width and turn on signed mode.
3. Read or copy the other two representations.

Frequently asked questions