Table of Contents
Advertisement
31 30
23 22
8-bit biased
S
exponent
Single Precision
63 62
11-bit biased
S
exponent
Table D-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.
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 larger than e
i.e. the implicit integer value b0 is equal to one. Note that this integer value is not stored in mem-
ory. Normalized numbers x are equal in value to:
where 1.f is a binary, fixed point number, i.e.:
Therefore, the smallest magnitude of any normalized number is equal to ( e=e
Using the value from Table D-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
Figure D-1. SP and DP 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 D-1 summarizes these values for SP and DP. If the biased ex-
( E is larger than E
min
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
min
max
+1
+254
+1
+2046
E
E
): For numerical values, the biased exponent
max
), the number in question is called normalized,
min
1.f
p-1
1
+...+ (–
)
• b
2
2
p-1
, f=0):
min
-38
for SP numbers.
=1, e=e
):
i
max
D-3
0
Advertisement
Table of Contents
