About

In systems architecture and embedded engineering, the hexadecimal system is the de facto standard for data representation. Unlike decimal, which is designed for biological counting (ten fingers), hexadecimal aligns perfectly with binary logic. One hex digit represents exactly one nibble (4 bits), and two hex digits represent one byte (8 bits). This alignment is critical when debugging memory dumps, analyzing network packets, or optimizing bitwise logic.

This tool is designed for high-stakes engineering. It bypasses standard floating-point limitations by utilizing BigInt logic, allowing for arbitrary precision conversion limited only by system memory. It addresses the common pain points of standard calculators: lack of bit-level visibility, confusion regarding endianness (byte order), and the opacity of floating-point storage formats (IEEE 754). Whether you are decoding a UTF-8 string from a raw buffer, verifying an IPv6 header, or reverse-engineering a binary file format, precision here is non-negotiable.

Formulas

Conversion relies on the positional notation of base-16. For a hex string H of length n, the integer value V is calculated as:

V = n−1∑i=0 d_i × 16ⁿ⁻¹⁻ⁱ

Where d_i is the decimal value of the digit at index i. For IEEE 754 Floating Point interpretation (32-bit), the bits are split into Sign (S), Exponent (E), and Mantissa (M):

Value = (−1)^S × 2^(E−127) × (1 + M)

Reference Data

Hex	Dec	Bin	Context / Standard / Magic Number
0x00	0	0000 0000	NULL (ASCII) / False
0x0A	10	0000 1010	LF (Line Feed)
0x20	32	0010 0000	Space (ASCII)
0x7F	127	0111 1111	Max Signed 8-bit Integer (Int8)
0xFF	255	1111 1111	Max Unsigned 8-bit Integer (Uint8)
0x100	256	1 0000 0000	2⁸
0xFFFF	65,535	16 ones	Max Uint16 / Port Limit
0x7FFF FFFF	2,147,483,647	31 ones	Max Int32 (Unix Year 2038 Problem)
0xFFFF FFFF	4,294,967,295	32 ones	Max Uint32 / IPv4 Limit
0x8950 4E47	...	...	PNG File Header
0xCAFE BABE	...	...	Java Class Magic Number
0x2540 BE400	10,000,000,000	...	10 Billion

Frequently Asked Questions

Endianness refers to the order in which bytes are stored in memory for multi-byte data types. "Big Endian" stores the most significant byte first (like reading left-to-right), while "Little Endian" (used by Intel/AMD x86 processors) stores the least significant byte first. Confusing these results in completely garbled data decoding.

We utilize the JavaScript BigInt primitive, which removes the safe integer limit (2^53 - 1) inherent in standard floating-point math. This allows for calculations involving IPv6 addresses (128-bit) or cryptographic keys (256-bit+) without precision loss.

Many simple calculators treat all numbers as floats, losing precision after 15 digits. Additionally, formatted inputs with spaces or "0x" prefixes can confuse basic parsers. This tool employs a strict sanitation layer before processing to ensure clean parsing.

Yes. The "Deep Analysis" section includes a UTF-8/ASCII decoder. It interprets the byte stream as character codes. Note that not all byte sequences are valid UTF-8; invalid sequences may show replacement characters.

In raw binary, bits are just bits. "Unsigned" treats all bits as magnitude (0 to Max). "Signed" (Two's Complement) uses the most significant bit as a sign flag. For example, 0xFF is 255 (Unsigned) but -1 (Signed 8-bit).