Operating instructions
D.
Octal Representation of Binary Numbers
11.
ARITHMETIC COMPUTATIONS IN BINARI
AND OCTAL
Because the base
"8" of the octal number
system
is
a power
of
2--the base of the A. Binary Arithmetic
binary system
--
three binary numbers may
be read
as
one octal number. This grouping
of binary numbers into octal representation
is
easier
to
read
than
straight binary. To
illustrate:
100111111000
=
binary form of the
decimal number 2552
The binary number
is
long and awkward to
read
or
copy, and cannot be easily converted
to decimal. The same binary number mav be
written in groups of three digits dividing from
the rightmost three
as
follows:
100
11
1
111
000,~~
reading each group as a binary number,
one
obtains: 4 7 7
0.
This smaller number
can be designated in octal as
47708.
E. Binary Coded Decimal
Besides using the number systems just des-
cribed, computers use a code called binary
coded decimal (BCD). The code represents
letters of the alphabet and symbols such as
dollar signs
as
well as decimal numbers.
There are several ways of ';codingJ' decimal
digits by combining binary digits to represent
one decimal digit. The code used with the
GE
225
is
often given in octal, as shown in
the third column of the table, Appendix D.
Each digit in octal stands for a three digit
binary number. The Fourth column of the
table, Appendix
D,
shows the code which is
physically on the tape, but
is
never used in
reading information into or out of the com-
puter. The reason for the information being
in a
Werent form on the tape
is
that it
is
then in a form usable with equipment by
manufacturers other than General Electric.
The table which follows contains a portion
of
the BCD code used in reading information into
or out of the computer.
1.
Addition:
o+
o=o
1+
0
=
1
1
+
1
=
10 (0
with
1
carried)
I
(carry)
1
11
0001 110110
+
0001
+
10111
00 10 100 110
1
2. Subtraction:
0-o=o
1
-
1=
0
1
-
o=
1
0
-
1
=
1
(with
1
borrowed)
Borrowing can be confusing in binary, and
there are several
ways of thinking of it. One
way
is
to think of each borrow as bringing
twice the value to a number from theposition
immediately to the left of it. For example,
binary positions double in value to the left,
as is seen by the position values:
16,
8,
4, 2,
1.
When borrowing a
"1"
from the
16
position and putting it in the 8 position,
it is the same as borrowing two
"1"s
for the
8 position. In turn, one can borrow one
of the borrowed
"
1"s
from the
8
position to
put two
"1"s
in the
4
position. The follow-
ing examples use this principle:
Position value=
16
8 4 2
1
Borrow
=
11
Borrow
=
zz2
Binary number,
1
fl
P)
0
1
(Decimal value
=
17)
Binary number-
1
0
1
0
(Decimal value
=
10)
Binary diff.
0
0
1 1 1
(Decimal
diff.
k-Fj)
Decimal Binary
Decimal
BCD Octal BCD Binary
Number
Representation Representation
Additional examples: