Bits of a Floating Point Value

The IEEE 754 representation of a floating point value:

• Sign bit is 0 for positive and 1 for negative.
• The exponent is stored with an offset. +127 for single precision and +1023 for double precision.
• The significand implicitly starts with a 1 followed by the binary point.

The value represented is:

Special Cases

• If all the exponent bits are zero, then −126 (or −1023 for a double) is the actual exponent, and the implicit leading bit of the significand is 0 (instead of 1). See Normal vs Subnormal Floats.

• If all the exponent bits are ones, then the value is infinity (if all the significand bits are zero) and NaN (if any significand bit is one).

• The sign of a zero value is ignored by all comparison operations (but may still have significance in other situations).

• For NaN the sign bit is always ignored.