Texas Instruments TMS320C3x 사용자 설명서
Floating-Point Formats
5-4
5.3
Floating-Point Formats
The ’C3x supports four floating-point formats:
-
A short floating-point format for immediate floating-point operands, consisting
of a 4-bit exponent, a sign bit, and an 11-bit fraction
of a 4-bit exponent, a sign bit, and an 11-bit fraction
-
(’C32 only) A short floating-point format for use with 16-bit floating-point
data types, consisting of a 2s-complement, 8-bit exponent field, a sign bit,
and a 7-bit fraction
data types, consisting of a 2s-complement, 8-bit exponent field, a sign bit,
and a 7-bit fraction
-
A single-precision floating-point format by an 8-bit exponent field, a sign
bit, and a 23-bit fraction
bit, and a 23-bit fraction
-
An extended-precision floating-point format consisting of an 8-bit exponent
field, a sign bit, and a 31-bit fraction.
field, a sign bit, and a 31-bit fraction.
All ’C3x floating-point formats consist of three fields:
an exponent field (e), a
single-bit sign field (s), and a fraction field (f ). The sign field and fraction field
may be considered as one unit and referred to as the
may be considered as one unit and referred to as the
mantissa field (man).
Figure 5–5. General Floating-Point Format
Exponent
Sign
Fraction
Mantissa
The general equation for calculating the value in a floating-point number is:
x
+
ss.f
2
2
e
In the equation,
s is the value of the sign bit, s is the inverse of the value of the
sign bit,
f is the binary value of the fraction field, and e is the decimal equivalent
of the exponent field.
The mantissa represents a normalized 2s-complement number. In a normalized
representation, a most significant nonsign bit is implied, thus providing an addi-
tional bit of precision. The implied sign bit is used as follows:
representation, a most significant nonsign bit is implied, thus providing an addi-
tional bit of precision. The implied sign bit is used as follows:
-
If
s = 0, then the leading two bits of the mantissa are 01.
-
If
s = 1, then the leading two bits of the mantissa are 10.
If the sign bit,
s, is equal to 0, the mantissa becomes 01.f
2
, where
f is the binary
representation of the fraction field. If
s is 1, the mantissa becomes 10.f
2
, where
f
is the binary representation of the fraction field.
For example, if f = 00000000001
2
and
s = 0, the value of the mantissa (man)
is 01.00000000001
2
. If
s = 1 for the same value of f, the value of man is
10.00000000001
2
.