Binary Notation; Octal Notation - IBM 709 General Information Manual

Figure 3. Main Computer Components
as punched card readers, a device to read or write on
magnetic or paper tape, a telephone or teletype line,
punched card recorders, and printing equipment.
An input component is any device capable of feed-
ing information into a computing and data handling
unit, usually called the central processing unit.
A storage unit must also be provided to store or
"remember" all input data and instructions (also
called orders) to the computer. These instructions are
then used to tell the computer how the processing of
data is to be executed.
The central processing unit has an arithmetic sec-
tion to accomplish all arithmetic and logical opera-
tions and a section to modify or change instructions
to adapt the processing to variations within the es-
tablished procedure. A control section is also a part
of the central processing unit and directs the com-
puter in its operation by making logical decisions. An
example of one of these decisions would be a test to
determine if a number is positive or negative. As a
result of this test, the computer can take a different
processing course for each alternative. Simple tests
may be combined to make complex logical decisions.
The output components are any devices capable of
recording the resultant data after the central process-
ing unit has operated upon it.
Binary Notation
The common decimal notation of the commercial and
scientific world is a familiar one. This notation is so
familiar that its use is hardly questioned. However,
it is possible that, for some purposes, other number-
ing systems are more convenient.
What numbering system to use is entirely a matter
of convenience. Decimal notation is used because it
is most familiar and is understood by most people.
However, had our primeval ancestors developed eight
fingers instead of ten, we would probably be more
familiar with a numbering system based on eight,
rather than ten, and we might consequently question
the decimal system.
6 IBM 709-7090
The decimal system, with its ten digits, is learned
by most people early in their training. This system
serves well for counting purposes. Why then should
computers designed to assist mathematicians, engi-
neers and businessmen, be designed to use the binary
system of numbers?
The reason is that current digital computers use
binary circuits; therefore, the mathematics of com-
puters is binary in nature. The octal system is a
shorthand method of writing long binary numbers.
Octal notation is used when discussing the computer,
but has no relation to the internal computer circuits.
The binary, or "base two" system, uses the two sym-
bols 0 and 1 to represent all quantities. Counting
starts in the same manner as in the decimal system
with a 0 for zero and then a I for one. At two, how-
ever, there are no more symbols to be used. It is
therefore necessary to take the same step at two in the
binary system that is taken at ten in the decimal sys-
tem. This step is to place a I in the next position
to the left and start again with a 0 in the original
position. A binary 10 is equivalent in this respect to
a 2 in the decimal system. Counting is continued in
an analogous manner with a carry to the next higher
order every time a two is reached instead of every
time a ten is reached. Counting in the binary system
is as follows:
Binar) Decimal Binary Decimal
8 4
2 1
84
2 1
0 = 0 1
=
1
1 0
-
2 1 1
-
3
100 -
4 1 0 1
-
5
1 1 0
-
6
11 1
=
7
1 0
o
0
-
8 1 0
o
1
-
9
Octal Notation
It has already been pointed out that binary numbers
require about three times as many positions as deci-
mal numbers to express the equivalent number. This
is not a problem to the computer itself, but in talking
and writing, these binary numbers are bulky. A long
string of ones and zeros cannot be effectively trans-
mitted from one individual to another. Some short-
hand method is necessary. The octal number system
fills this need. Because of its simple relationship to
binary, numbers can be converted from one system to
another by inspection. The base of the octal system
is 8. This means there are eight symbols: 0, 1, 2, 3,
4, 5, 6, and 7. There are no 8's or 9's. The important
relationship is that three binary positions are equiva-
lent to one octal position. The following table com-
bines what has been shown concerning decimal and
binary with the octal numbers.