<s>
In	O
IEEE	O
754	O
floating-point	B-Algorithm
numbers	I-Algorithm
,	O
the	O
exponent	O
is	O
biased	O
in	O
the	O
engineering	O
sense	O
of	O
the	O
word	O
–	O
the	O
value	O
stored	O
is	O
offset	O
from	O
the	O
actual	O
value	O
by	O
the	O
exponent	B-Algorithm
bias	I-Algorithm
,	O
also	O
called	O
a	O
biased	B-Algorithm
exponent	I-Algorithm
.	O
</s>
<s>
Biasing	O
is	O
done	O
because	O
exponents	O
have	O
to	O
be	O
signed	O
values	O
in	O
order	O
to	O
be	O
able	O
to	O
represent	O
both	O
tiny	O
and	O
huge	O
values	O
,	O
but	O
two	B-General_Concept
's	I-General_Concept
complement	I-General_Concept
,	O
the	O
usual	O
representation	O
for	O
signed	O
values	O
,	O
would	O
make	O
comparison	O
harder	O
.	O
</s>
<s>
By	O
arranging	O
the	O
fields	O
such	O
that	O
the	O
sign	O
bit	O
takes	O
the	O
most	O
significant	O
bit	O
position	O
,	O
the	O
biased	B-Algorithm
exponent	I-Algorithm
takes	O
the	O
middle	O
position	O
,	O
then	O
the	O
significand	B-Algorithm
will	O
be	O
the	O
least	O
significant	O
bits	O
and	O
the	O
resulting	O
value	O
will	O
be	O
ordered	O
properly	O
.	O
</s>
<s>
This	O
is	O
the	O
case	O
whether	O
or	O
not	O
it	O
is	O
interpreted	O
as	O
a	O
floating-point	B-Algorithm
or	O
integer	O
value	O
.	O
</s>
<s>
The	O
purpose	O
of	O
this	O
is	O
to	O
enable	O
high	O
speed	O
comparisons	O
between	O
floating-point	B-Algorithm
numbers	I-Algorithm
using	O
fixed-point	O
hardware	O
.	O
</s>
<s>
To	O
calculate	O
the	O
bias	O
for	O
an	O
arbitrarily	O
sized	O
floating-point	B-Algorithm
number	I-Algorithm
apply	O
the	O
formula	O
2k−1−1	O
where	O
k	O
is	O
the	O
number	O
of	O
bits	O
in	O
the	O
exponent	O
.	O
</s>
<s>
When	O
interpreting	O
the	O
floating-point	B-Algorithm
number	I-Algorithm
,	O
the	O
bias	O
is	O
subtracted	O
to	O
retrieve	O
the	O
actual	O
exponent	O
.	O
</s>
<s>
The	O
floating-point	B-Algorithm
format	I-Algorithm
of	O
the	O
IBM	B-Device
704	I-Device
introduced	O
the	O
use	O
of	O
a	O
biased	B-Algorithm
exponent	I-Algorithm
in	O
1954	O
.	O
</s>
