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This special feature provides the 1620 with the ability
to do floating-point' arithmetic, using floating-point
instructions instead of program sub-routines.
The use of automatic floating-point operations can
result in a 50 to 100 per cent increase in the com-
puting power of the 1620
CPU,
depending on the
amount of floating-point computations required. Also,
up to 15 per cent of the basic 1620 core-storage
capacity can be saved through the elimination of
subroutines and call sequence instructions associated
with Floating Add, Floating Subtract, Floating Mul-
tiply, and Floating Divide.
The Automatic Division special feature is a pre-
requisite to the installation of Automatic Floating
Point Operations.
floating-Point Arithmetic
Scientific and engineering computations frequently
involve lengthy and complex calculations in which
it is necessary to manipulate numbers that may vary
Widely in magnitude. To obtain a meaningful answer,
problems of this type usually require that as many
significant digits as possible be retained during cal-
culation and that the decimal point always be prop-
erly located. When applying such problems to a
computer, several factors must be taken into con-
sideration, the most important of which is decimal
point location.
Generally speaking, a computer does not recognize
the decimal point present in any quantity used during
the calculation. Thus, a product of 414154 will re-
sult regardless of whether the factors are 9.37 x 44.2,
93.7 x .442, or 937 x 4.42, etc. It is the programmer's
responsibility to be cognizant· of the decimal point
location during and after the calculation and to ar-
range the program accordingly. In a floating-add
operation, for example, the decimal point of all num-
bers must be lined up to obtain the correct sum. To
facilitate this arrangement, the programmer must
shift the quantities as they are added. In the manip-
ulation of numbers that vary greatly in magnitude,
the resulting quantity could conceivably exceed al-
lowable working limits.
The processing of numbers expressed in ordinary
form, e.g., 427.93456, 0.0009762, 5382, -623.147,
3.1415927, etc., can be accomplished on a computer
only by extensive anaylsis to determine the size and
Automatic Floating-Point Operations
range of intermediate and final results. This anaylsis
and subsequent number scaling frequently takes
longer than does the actual calculation. Furthermore,
number scaling requires complete and accurate in-
formation as to the boundaries of all numbers that
come into the computation (input, intermediate, out-
put). Since it is not always possible to predict the
size of all numbers in a given calculation, anaylsis
and number scaling are sometimes impractical.
To alleviate this programming problem, a system
must be employed in which information regarding
the magnitude of all numbers accompanies the quan-
tities in the calculation. Thus, if all numbers are
represented in some standard, predetermined for-
mat which instructs the computer in an orderly and
simple fashion as to the location of the decimal pOint,
and if this representation is acceptable to the routine
doing the calculation, then quantities which range
from minute fractions having many decimal places
to large whole numbers having many integer places
can be handled. The arithmetic system most com-
monly used, in which all numbers are expressed in a
format having the above feature, is called-. "floating-
point arithmetic."
The notation used in floating-point arithmetic is
basically an adaptation of the scientific notation
widely used today. In scientific work,. very large or
very small numbers are expressed as a number, be-
tween one and ten, times a power of ten. Thus
427.93456 is
written
as
4.2793456 x 10
2
and
0.0009762 as 9.762 x 10-
4
•
In the 1620 floating-pOint
arithmetic system, the range of numbers is modified
to extend between .1 and .99999999; that is, the deci-
mal point of all numbers is placed to the left of the
high-order (leftmost) nonzero digit. Hence, all quan-
tities may be thought of as a decimal fraction times
a power of ten (e.g., 427.93456 as .42793456 x 10
3
and 0.0009762 as .97620000 x 10-
3 )
where the frac-
tion is called the mantissa, and the power of ten,
used to indicate the number of places the decimal
point was shifted, the exponent. In addition to the
advantages inherent in scientific notation, the use
of floating-point numbers during processing elimi-
nates the necessity of analyzing the operations to
determine the positioning of the decimal point in
intermediate and final results, since the decimal point
is always immediately to the left of the high-order
nonzero digit in the mantissa.
23
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