The model set for reals, in general, is defined as one of the following:

The following values apply to this model set:

*x*is the real value.*s*is the sign (either +1 or -1).*b*is the base (real radix; an integer greater than 1).*p*is the number of mantissa digits (an integer greater than 1). The number of digits differs depending on the real format, as follows:

IEEE S_floating 24 Compaq ^{1}VAX F_floating^{2}24 IEEE T_floating 53 Compaq VAX D_floating ^{2}53 ^{3}Compaq VAX G_floating ^{2}53 ^{1}Formerly DIGITAL

^{2}VMS only

^{3}The memory format for VAX D_floating format is 56 mantissa digits, but computationally it is 53 digits. It is considered to have 53 digits by Compaq Fortran.*e*is an integer in the range*e*_{min}to*e*_{max}, inclusive. This range differs depending on the real format, as follows:

*e*_{min}*e*_{max}IEEE S_floating -125 128 Compaq VAX F_floating ^{1}-127 127 IEEE T_floating -1021 1024 Compaq VAX D_floating ^{1}-127 127 Compaq VAX G_floating ^{1}-1023 1023 ^{1}VMS only*f*_{k}is a nonnegative number less than*b*(*f*_{1}is also nonzero).

For * x = 0*, its exponent *e* and digits *f*_{k}
are defined to be zero.

The model set for single-precision real (REAL(4) or REAL*4) is defined as one of the following:

The following example demonstrates the general real model for
*x* = 20.0 using a base (*b*) of 2:

*x* = 1 x 2^{5} x (1 x 2^{-1} + 0 x 2^{-2} + 1 x 2^{-3})

*x* = 1 x 32 x (.5 + .125)

*x* = 32 x (.625)

*x* = 20.0

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