Advertisement
Chapter·· 9.. Floating-Point· Instructions
Contents
FIOliting-Poiht Number Representation
Normalization
9:'2
9-2
9-4
COMPARE
9:'8
LOAD
9-8
9-9
9:'10
9-6
9-1
Floating-point instructions are used toperforni
calculations on operands with a wide range of
magnitude. and to yield results scaled to preserve
precision;
The floating-point instructions provide for
loading, rounding, adding, subtracting, comparing,.
multiplying, dividing, and storing; as well· as
controlling the sign of short, long; and extended
operands. Short operands generally permit faster
processing and require less storag.e· than long or
extended operands. On the other hand; long and
extended operands. permit greater precision in
computation. Four fl()ating.;.point registers are
provided. Instructions may perform either
register-to-register. or storage-and-register
operations.
Most of the instructions generate normalized
results, which preserve the highest precision in the
operation. For addition ·and subtraction,.
instructions· are also· provided that generate
unnormalized
results~
Either nortualizedor
unnormalizecl numbers may be used as operands for
any floating-point ()peration;
Floating-Point Number Representation
A floating-point number consists of a signed
hexadecimal fraction and an unsigned seven-bit
binary integer called the characteristic. The
characteristic represents a signed exponent and is
obtained by adding 64 to the exponent value
(excess-64 notation). The range of the
9-10
9-10
LOAD NEGATIVE
9-11
9-11
9-11
9-12
9-13
SUBTRACT UNNORMALIZED
9-14
9-14
characteristic is 0 to 127, which corresponds to an
exponent range of -64 to +63. The value of a
floating-point number is the product of its fraction
and the number 16 raised to the power of the
exponent which is represented by its characteristic.
The fraction of a floating-point number is
treated as a hexadecimal number because it is
considered to be multiplied by a. number which is a
power of 16. The name, fraction, indicates that the
radix point is assumed to be immediately to the left
of the leftmost fraction digit. The fraction is
represented by its absolute value. and . a separate
sign bit. The entire number is positive or negative,
depending on whether the sign bit of the fraction is
zero or one, respectively.
When a floating-point operation would cause the
result exponent to exceed 63, the characteristic
wraps around from 127 to 0, and an
exponent-ove:fflow condition exists. Theresult
characteristic is then too small by 128. When an
operation would cause the exponent to be less than
-64, the characteristic wraps around from 0 to 127,
and an exponent-underflow condition exists. The
result characteristic is then too large by 128, except
that a zero characteristic is produced when a true
zero is forced.
A true zero is a floating-point number with a
zero characteristic, zero fraction,and plus sign. A
true zero may arise as the normal result of an
arithmetic operation because of the particular
Chapter 9 . Floating-Point Instructions
9-1
Advertisement
Chapters
