Freescale Semiconductor MC68881 - Binary Real Data Formats

3
Since all FPCP internal operations are performed in full extended precision format, signed
integer operands are converted to extended precision values before the specified operation
is performed. Thus, mixed mode arithmetic is implicitly supported.
3.2 BINARY REAL DATA FORMATS
Floating-point numbers can be encoded in any of three binary real data formats: single
precision (32 bits), double precision (64 bits), and double-extended precision (96 bits, 80
of which are used). All three of these formats fully comply with the
IEEE Standard for
Binary Floating-Point Arithmetic.
NOTE
The single-extended precision data format defined in the IEEE standard is redun-
dant in a device that supports the double-extended precision format. Thus, all
references in this manual to extended precision imply double-extended precision
as defined by the IEEE standard.
Since all FPCP internal operations are performed in extended precision, single and double
precision operands are converted to extended precision values before the specified operation
is performed. Thus, mixed mode arithmetic is implicitly supported. The memory formats
for the real data formats are shown in Figure 3-2.
The exponent in all three binary formats is an unsigned binary integer with an implied
bias added to it. The bias values for single, double, and extended precision are 127, 1023,
and 16383, respectively. When the bias is subtracted from the value of the exponent, the
result represents a signed twos-complement power of two that yields the magnitude of a
normalized floating-point number when multiplied bythe mantissa. Since biased exponents
are used, a program can execute an integer compare instruction (CMP) to compare floating-
point numbers in memory (regardless of the absolute magnitude of the exponents).
30 22 0
g-BIT 23-~T I ~':~ F-.~L
EXPONENT ERAC'I10N
I-- SIGN OF FRAC'I10N
94 80
I 15-•1T
62 51
l l-BiT
II EXPONENT I
/
SiGN OF FRACT1CIN
0
FRACTION
I
63
64-BIT
MANTISSA
-- IMPLICIT BINARY P01NT
Figure 3-2. Binary Real Data Formats
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FREESCALE
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MC68881/MC68882 USER'S MANUAL