The Exponent

The eight bits 23 through 30 contain the exponent. The exponent is an integer, but may be negative, zero, or positive. You might guess that an 8-bit two's complement integer would work perfectly for this, but a different type of notation is used.

The exponent is expressed using a biased integer. The true exponent is added to +12710 resulting in an unsigned binary integer. The biased integer is encoded using 8-bit unsigned binary.

• A biased exponent of +127 represents the actual exponent 0.
• A biased exponent of +128 represents the actual exponent 1.
• A biased exponent of +126 represents the actual exponent -1.

Exceptions: (1) A floating point value of 0.0 is represented with a mantissa of 23 zero bits and an exponent of 8 zero bits. It is not legal to have an exponent of zero with a non-zero mantissa. (2) The exponent 25510 (1111 1111) is used to signal various problems, such as division by zero.