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may be used directly for input and output in the
extended binary-cod ed-decimal interchange code
(EBCDIC), except that the sign must be separated
from the rightmost digit and handled as a separate
character. For positive (unsigned) numbers,
however, the sign code of the rightmost digit can
simply be replaced by the zone code, which is one
of the acceptable alternate codes for plus.
In either format, negative decimal integers are
represented in true notation with a separate sign.
As for binary integers, the radix point (decimal
point) of decimal integers is considered to be fixed
at the right, and any scaling is done by the
programmer.
The following are some examples of decimal
integers shown in hexadecimal notation:
Value
Packed Format
Zoned Format
+123
12 3C
F1 F2 C3 or F 1 F2
-4321
04 32 10
F4 F3 F2 01
+000050
00 00 05 OC
Fa Fa Fa Fa F5 CO
Fa Fa Fa Fa F5 Fa
-7
70
07
00000
00 00 OC
Fa Fa Fa Fa
co
or
Fa Fa Fa Fa Fa
F3
or
Under some circumstances, a zero with a minus
sign (negative zero) is produced. For example, the
multiplicand:
00 12 3D
(-123)
times the multiplier:
OC
(+0)
generates the product:
00 OOOD
(-0)
because the product sign follows the algebraic rule
of signs even when the value is zero. A negative
zero, however, is entirely equivalent to a positive
zero; they compare equal in a decimal comparison.
Floating-Point Numbers
A floating-point number is expressed as a fraction
multiplied by a separate power of 16. The term
floating point indicates that the radix-point
placement, or scaling, is auto-matically maintained
by the machine.
The part of a floating-point number which
represents the significant digits of the number is
called the. fraction. A second part specifies the
power (exponent) to which 16 is raised and
indicates the location of the radix point of the
number. The fraction and exponent may be
A~4
IBM 4300 ProcessorsPrincipies of Operation
represented by 32 bits (short format), 64 bits (long
format), or 128 bits (extended format).
Short Floating-Point Number
~r-----------~---------/--------~
IslCharacteristicl6-0igit Fri_c_t_i_o_n ____
~
a
1
8
31
Long Floating-Point Number
~,-----------~---------/----------~
IslCharacteristicl14-0igit F/_a_ct __ io_n ______
~
a
1
8
63
Extended Floating-Point Number
High-Order Part
~------------~---------/----------~
High-Order
Leftmost 14
~igits
S Characteristic
of 28-Digit Fraction
~------------~---------/----------~
a
8
63
Low-Order Part
~~----------~---------/-----------.
Low-Order
Rightmost 14 Digits
S Characteristic
of 28-0igit Fraction
~~----------~---------/----------~
64
72
127
A floating-point number has two signs: one for
the fraction and one for the exponent. The
fraction sign, which is also the sign of the entire
number, is the leftmost bit of each format (0 for
plus, 1 for minus). The numeric part of the
fraction is in true notation regardless of the sign.
The numeric part is contained in bits 8-31 for the
short format, in bits 8-63 for the long format, and
in bits 8-63 followed by bits 72-127 for the
extended format.
The exponent sign is obtained by expressing the
exponent in excess-64 notation; that is, the
exponent is added as a signed number to 64. The
resulting number is called the characteristic. It is
located in bits 1-7 for all formats. The
characteristic can vary from 0 to 127, permitting
the exponent to vary from -64 through 0 to +63.
This provides a scale multiplier in the range of
16-
64
to 16+
63 .
A nonzero fraction, if normalized,
must be less than one and greater than or equal to
1/16, so that the range covered by the magnitude
M of a floating-point number is:
16-
65
$
M
<
16
63
In decimal terms:
16-
65
is approximately equal to 5.4 x 10-
79
16
63
is approximately equal to 7.2 x 10
75
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