63 62
s
52 51
0
e
f
Figure 6.2 Format of Double-Precision Floating-Point Number
The exponent is expressed in biased form, as follows:
e = E + bias
The range of unbiased exponent E is Emin – 1 to Emax + 1. The two values Emin – 1 and Emax + 1 are
distinguished as follows. Emin – 1 indicates zero (both positive and negative sign) and a
denormalized number, and Emax + 1 indicates positive or negative infinity or a non-number (NaN).
Table 6.1 shows bias, Emin, and Emax values.
Table 6.1 Floating-Point Number Formats and Parameters
Parameter
Total bit width
Sign bit
Single-Precision
32 bits
1 bit
Double-Precision
64 bits
1 bit
Exponent field
Fraction field
Precision
Bias
8 bits
11 bits
23 bits
24 bits
+127
52 bits
53 bits
+1023
Emax
+127
+1023
Emin
–126
–1022
Floating-point number value v is determined as follows:
If E = Emax + 1 and f ≠ 0, v is a non-number (NaN) irrespective of sign s
If E = Emax + 1 and f = 0, v = (–1)s (infinity) [positive or negative infinity]
If Emin ≤ E ≤ Emax , v = (–1)s2E (1.f) [normalized number]
If E = Emin – 1 and f ≠ 0, v = (–1)s2Emin (0.f) [denormalized number]
If E = Emin – 1 and f = 0, v = (–1)s0 [positive or negative zero]
Table 6.2 shows the ranges of the various numbers in hexadecimal notation.
Rev. 6.0, 07/02, page 162 of 986
RENESAS [ RENESAS TECHNOLOGY CORP ]
