Converting Between Float and Hex Representation

Converting between decimal floating-point values and their hexadecimal byte representation is a common task when debugging binary data, examining memory dumps, or implementing binary protocols.

Float32 to hex — step by step for 42.0:

1. Convert 42 to binary: 101010.0
2. Normalize: 1.01010 x 2^5
3. Sign = 0, Exponent = 5 + 127 = 132 = 10000100, Mantissa = 01010000...0
4. Full binary: 0 10000100 01010000000000000000000
5. Group into 4-bit nibbles: 0100 0010 0010 1000 0000 0000 0000 0000
6. Convert nibbles to hex: 4 2 2 8 0 0 0 0
7. Result: 0x42280000

Hex to float — step by step for 0x42280000:

1. Convert hex to binary: 0100 0010 0010 1000 0000 0000 0000 0000
2. Extract fields: sign = 0, exponent = 10000100 = 132, mantissa = 01010000...0
3. Actual exponent = 132 - 127 = 5
4. Significand = 1.01010 (binary) = 1 + 0.25 + 0.0625 = 1.3125
5. Value = (-1)^0 x 1.3125 x 2^5 = 1 x 1.3125 x 32 = 42.0

Using JavaScript to convert:

// Float to hex
function floatToHex(value) {
  const buf = new ArrayBuffer(4);
  new DataView(buf).setFloat32(0, value);
  return '0x' + new DataView(buf).getUint32(0).toString(16).padStart(8, '0');
}

// Hex to float
function hexToFloat(hex) {
  const buf = new ArrayBuffer(4);
  new DataView(buf).setUint32(0, parseInt(hex, 16));
  return new DataView(buf).getFloat32(0);
}

// Double to hex
function doubleToHex(value) {
  const buf = new ArrayBuffer(8);
  new DataView(buf).setFloat64(0, value);
  const hi = new DataView(buf).getUint32(0).toString(16).padStart(8, '0');
  const lo = new DataView(buf).getUint32(4).toString(16).padStart(8, '0');
  return '0x' + hi + lo;
}

Common hex patterns to recognize:

Pattern	Float32	Meaning
0x00000000	+0	All bits zero
0x80000000	-0	Only sign bit set
0x3F800000	1.0	The unit value
0x7F800000	+Infinity	Max exponent, zero mantissa
0x7FC00000	NaN	Max exponent, non-zero mantissa
0x7F7FFFFF	3.40e+38	Largest finite float32

Endianness matters:

When reading floats from binary files or network packets, the byte order depends on the platform. Big-endian (network byte order) stores the most significant byte first. Little-endian (x86) stores the least significant byte first. The hex values shown here are in big-endian order.