Hex to Double Converter

A standard IEEE 754 double contains 64 bits. Since every hexadecimal digit represents four binary bits, those 64 bits can be represented compactly using exactly sixteen hexadecimal digits.

This converter does not treat the hexadecimal input as an ordinary base-16 integer. Instead, it places the eight hexadecimal bytes into a 64-bit floating-point buffer and interprets the resulting bit pattern as a binary64 double.

Sign bit

The most significant bit is the sign. A sign bit of 0 represents a positive value, while a sign bit of 1 represents a negative value.

Exponent field

Eleven bits store the exponent. For ordinary normalized numbers, the stored exponent uses a bias of 1023. Subtracting 1023 from the encoded exponent provides the unbiased binary exponent.

Fraction field

The remaining 52 bits store the fraction portion of the significand. Normal values also assume an implicit leading binary 1, providing approximately 53 bits of significand precision.

1. Validate the hexadecimal pattern

A full IEEE 754 binary64 representation contains eight bytes, equivalent to sixteen hexadecimal digits. The optional prefix 0x can be removed before decoding.

2. Convert each pair of hex digits into a byte

Sixteen hexadecimal characters create eight bytes. For example, 40 29 00 00 00 00 00 00 represents the canonical byte sequence for double value 12.5.

3. Interpret the bytes as Float64

The eight bytes are placed into an IEEE 754 64-bit floating-point buffer. The same bits can then be interpreted directly as a double-precision numeric value.

4. Decode individual fields

The converter also converts the hexadecimal pattern to binary so the sign bit, 11-bit exponent, and 52-bit fraction can be inspected independently.

Raw binary is precise but difficult to read because a double requires 64 individual zeros and ones. Hexadecimal compresses every four bits into one symbol, reducing a 64-bit pattern to only sixteen characters.

This makes hexadecimal particularly useful when examining floating-point values in debuggers, packet captures, memory dumps, binary files, firmware, serialization formats, and low-level programming.

Decimal 0.1 cannot be represented exactly as a finite binary fraction. Its base-2 representation repeats indefinitely, just as one-third repeats indefinitely in decimal notation.

IEEE 754 binary64 has finite precision, so it stores the closest representable binary value. That bit pattern is commonly written in hexadecimal as 3FB999999999999A.

Software normally displays that stored value as 0.1 because decimal formatting algorithms choose a compact representation that round-trips to the same binary64 number.

Subnormal doubles

A zero exponent field combined with a nonzero fraction indicates a subnormal number. Subnormal values fill the gap between zero and the smallest normal binary64 value.

This converter expects the conventional hexadecimal representation with the most significant byte first. For example, double value 12.5 is represented canonically as 4029000000000000.

Broken into bytes, this becomes: 40 29 00 00 00 00 00 00.

A little-endian memory dump may show the same bytes in reverse order: 00 00 00 00 00 00 29 40.

Using only eight hex digits

Eight hexadecimal digits normally represent a 32-bit IEEE 754 single-precision float, not a 64-bit double. Binary64 requires sixteen hexadecimal digits.

Treating hex as an integer

Parsing 4029000000000000 as an integer produces a completely different meaning. The bits must be reinterpreted as floating-point data rather than numerically converted from base 16.

Reversed byte order

Hex copied directly from little-endian memory can have reversed bytes compared with the conventional representation shown by floating-point references.

Assuming every bit pattern is a finite number

Some patterns intentionally represent positive or negative zero, infinity, NaN, or subnormal values.