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31 30
23 22
8-bit biased
S
exponent
Single Precision (SP)
63 62
11-bit biased
S
exponent
Table C-1. Parameters for Numerical Formats
There are 23 fractional bits (p=24) (bits 0 through 22) in the SP format, and 52 fractional bits
(p=53) (bits 0 through 51) in the DP format. Note that bit b
The sign bit, exponent, and fraction fields encode the numerical values of floating-point numbers, as well as
0,
, and NaNs as follows:
1. Normalized Numerical Values ( E
e lies between e
E
and E
min
max
ponent e is equal to or greater than e
called normalized ( i.e. the implicit integer value b0 is equal to one). Note that this integer value,
b
, is not stored in memory. Normalized numbers x are equal in value to:
0
where 1.f is a binary, fixed point number, i.e.:
Therefore, the smallest magnitude of any normalized number, X
Using the value from Table C-1, this equals approximately 1.18 • 10
The largest normalized numerical value that can be represented equals (all b
MOTOROLA
23-bit fraction
52 51
52-bit fraction
Double Precision (DP)
Figure C-1. SP and DP IEEE Formats
p-1
bias
SP
23
127
DP
52
1023
f = •b
b
•••b
1
2
p-1
min
and e
, inclusive. Equivalently, the exponent E takes on values between
min
max
inclusive. Table C-1 summarizes these values for SP and DP. If the biased ex-
s
e - bias
x = (-1)
• 2
1.f = 1+(o.5) • b
+ (0.25) • b
1
e min - bias
x
= 1 • 2
min,n
DSP96002 USER'S MANUAL
0
e
e
E min
min
max
+1
+ 254 - 126 + 127
+1
+2046 -1022 +1023
is not explicitly represented.
0
E
E
): For numerical values, the biased exponent
max
( E is greater than E
min
1.f
p-1
1
+...+ (–
)
• b
2
2
p-1
E min
= 1• 2
E max
), the number in question is
min
, is equal to ( e=e
min, n
min
-38
for SP numbers.
=1, e=e
i
max
0
, f=0):
):
C-3
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