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.
+127represents the actual exponent 0.
+128represents the actual exponent 1.
+126represents the actual exponent -1.
(1) A floating point value of
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
(1111 1111) is used
to signal various problems,
such as division by zero.
What is the mantissa when the entire float is zero?