Representation of 500.0 in IEEE32 Format

The exponent in IEEE32 has a fixed offset of 127 to always have positive values:

exp (500.0,IEEE32) = 8+127 == 87 (hex) ==  10000111 (bin)

The fields must be put together as shown the following listing:

Listing: Representation of decimal 500.0 in IEEE32



500.0 (dec) =
  0 (sign) 10000111 (exponent)

  11110100000000000000000 (mantissa) (IEEE32 as bin)

  0100 0011 1111 1010 0000 0000 0000 0000 (IEEE32 as bin)

  43 fa 00 00 (IEEE32 as hex)

The IEEE32 representation of decimal -500 is shown in the following listing.

Listing: Representation of decimal -500.0 in IEEE32


-500.0 (dec) =

  1 (sign) 10000111 (exponent)

  11111010000000000000000 (mantissa) (IEEE32 as bin)

  1100 0011 1111 1010 0000 0000 0000 0000 (IEEE32 as bin)

  C3 fa 00 00 (IEEE32 as hex)

Note: The IEEE formats recognize several special bit patterns for special values. The number 0 (zero) is encoded by the bit pattern consisting of zero bits only. Other special values such as "Not a number", "infinity", -0 (minus zero) and denormalized numbers do exist. For more information, refer to the IEEE standard documentation. Except for the 0 (zero) and -0 (minus zero) special formats, not all special formats may be supported for specific backends.