### ARITHMETIC CALCULATION IN COMPUTERS

__ARITHMETIC OPERATION AND CONVERSION DONE BY COMPUTER__

As we have seen in previous
post that arithmetic computation is an important thing in calculation, if a
person doesn’t know arithmetic computations,
he will be doomed to be in trouble during calculations that happens in everyday life. So it is necessary to learn arithmetic
computation. So in this post I am going
to take one step further. I am going to
write about octal and hexadecimal numbers.

Now let us discuss some
arithmetic conversion. Let us see what
is octal and hexadecimal numbers used by digital computer.

The conversion from and to
binary, octal and hexadecimal plays an important part in digital
computers. Since 2

^{3}= 8 and 2^{4}= 16 each octal digit corresponds to three binary digits and each four binary digit corresponds to one hexadecimal digit.
The conversion of from binary
to octal is easily accomplished by partitioning the binary into group of three
digit each, starting from binary point and preceding to the left or to the
right.

The corresponding octal digit
is then assigned to each group. The
following example illustrates the
procedure.

__10__

__110__

__001__

__101__

__011__.

__111__

__100__

__000__

__110__= (26153.406)

_{2}

2
6 1 5
3 7 4
0 6

Conversion from binary to
hexadecimal is similar, except that the
binary number is divided into group of four digits:

__10__

__1100__

__0110__

__1011__.

__1111__

__0010__= (2C6B.F2)

_{16}

2
C 6 B F 2

The corresponding hexadecimal
(or octal) digit for each group of binary digits is easily remembered after
studying the values.

Conversion from octal or
hexadecimal to binary is done by procedure reverse to the above. Each octal digit is converted to three bit binary equivalent
. Similarly, each hexadecimal digit is converted to its four-digit binary
equivalent.

Binary numbers are difficult to
work with because they require three or four times as many digits as their
decimal equivalent . For example, the
binary number 111111111111 is equivalent to decimal number 4095.
However, digital computers use binary numbers and its sometimes
necessary for human user to communicate directly to with the machine by means
of binary numbers.

One scheme that retains
binary system in the computer but reduces the number of
digits human must consider utilizes the relationship between binary number system and octal and
hexadecimal system. By this method, the
human thinks of the number of octal and hexadecimal numbers
and performs required conversion by inspection when direct communication
by the machine is necessary. Thus the
binary numbers 111111111111 is 12 digit and is expressed in octal as 7777 (four
digits) and while it is expressed in hexadecimal as FFF (3 digits).

During communication between
people (about binary numbers in the computer), the octal or hexadecimal
representation is more desirable because it can be represented in third or
quarter of number of digits required for equivalent binary number.

When the human communicates
with the machine (through console switches or indicator lights or by means of
programs written in machine language),
the conversion from octal or hexadecimal to binary and vice versa is done by inspection
by the human user.

Thank
you for reading

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