MOTOROLA
DSP96002 USER’S MANUAL
C-3
Figure C-1. SP and DP IEEE Formats
31 30
23 22
0
S
8-bit biased
exponent
23-bit fraction
Single Precision (SP)
Double Precision (DP)
S
11-bit biased
exponent
52-bit fraction
63 62
52 51
0
p-1
bias
e
min
e
max
E
min
E
max
SP
23
127
+1
+ 254 - 126
+ 127
DP
52
1023
+1
+2046 -1022
+1023
Table C-1. Parameters for Numerical Formats
f = •b
1
b
2
•••b
p-1
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
0
is not explicitly represented.
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
min
≤
E
≤
E
max
): For numerical values, the biased exponent
e
lies between
e
min
and
e
max
, inclusive. Equivalently, the exponent
E
takes on values between
E
min
and
E
max
inclusive. Table C-1 summarizes these values for SP and DP. If the biased ex-
ponent
e
is equal to or greater than
e
min
(
E
is greater than
E
min
), the number in question is
called normalized ( i.e. the implicit integer value b0 is equal to one). Note that this integer value,
b
0
, is not stored in memory. Normalized numbers x are equal in value to:
x = (-1)
s
• 2
e - bias
1.f
where
1.f
is a binary, fixed point number, i.e.:
1.f = 1+(o.5) • b
1
+ (0.25) • b
2
+...+ (–
1
2
)
p-1
• b
p-1
Therefore, the smallest magnitude of any normalized number, X
min, n
, is equal to (
e=e
min
, f=0):
x
min,n
= 1 • 2
emin - bias
= 1• 2
Emin
Using the value from Table C-1, this equals approximately 1.18 • 10
-38
for SP numbers.
The largest normalized numerical value that can be represented equals (all
b
i
=1, e=e
max
):
Summary of Contents for DSP96002
Page 3: ...1 2 DSP96002 USER S MANUAL MOTOROLA ...
Page 38: ...MOTOROLA DSP96002 USER S MANUAL 3 15 Figure 3 4 Modulo Arithmetic Unit Block Diagram ...
Page 39: ...3 16 DSP96002 USER S MANUAL MOTOROLA ...
Page 53: ...4 14 DSP96002 USER S MANUAL MOTOROLA ...
Page 76: ...MOTOROLA DSP96002 USER S MANUAL 5 23 Figure 5 8 Address Modifier Summary ...
Page 86: ...6 10 DSP96002 USER S MANUAL MOTOROLA ...
Page 101: ...MOTOROLA DSP96002 USER S MANUAL 7 15 Figure 7 9 HI Block Diagram One Port ...
Page 140: ...7 54 DSP96002 USER S MANUAL MOTOROLA ...
Page 166: ...9 10 DSP96002 USER S MANUAL MOTOROLA ...
Page 181: ...MOTOROLA DSP96002 USER S MANUAL 10 15 Figure 10 8 Program Address Bus FIFO ...
Page 337: ...MOTOROLA DSP96002 USER S MANUAL A 149 ...
Page 404: ...A 216 DSP96002 USER S MANUAL MOTOROLA PC xxxx D ...
Page 460: ...A 272 DSP96002 USER S MANUAL MOTOROLA SIOP Not affected ...
Page 484: ...A 296 DSP96002 USER S MANUAL MOTOROLA SSH PC SSL SR SP 1 SP ...
Page 519: ...MOTOROLA DSP96002 USER S MANUAL A 331 ...
Page 718: ...MOTOROLA DSP96002 USER S MANUAL B 199 ...
Page 871: ... MOTOROLA INC 1994 MOTOROLA TECHNICAL DATA SEMICONDUCTOR M Addendum ...
Page 888: ...MOTOROLA INDEX 1 INDEX ...
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