Representation Of DATA / INFORMATION
There is base or radix that used distinct symbols do digit.
Numbers are represented by a string digit symbols. For example Binary 0, 1 and
base is 2. Decimal 0, 1, 2 … 9 and base is 10. Octal 0, 1, 2 … 7 and base is 8.
Hexadecimal 0, 1, 2 … 9, A, B, C, E, F and base is 16.
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Binary Number System
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Octal Number System
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Decimal Number System
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Hexadecimal Number System
Binary Number System
It is a number system which base or radix is only 2.
As its name implies it supports only two numbers namely 0 and 1. Any value in
this number system is represented like this (1000)2. Here
base 2 shows that is a Binary number system.
Decimal
Number
|
Binary
Number
|
0
|
0000
|
1
|
0001
|
2
|
0010
|
3
|
0011
|
4
|
0100
|
5
|
0101
|
Here we will see some samples
of Binary number of a certain Decimal number.
Octal Number System
This very number system uses
eight digits, 0 1, 2, 3, 4, 5, 6, and 7. It is also called base eight numbered
system. Each position in an octal number represent a 0 power of the base (8)
for e.g.80 Last position in an octal number represent a x power of the base
(8), for e.g. 8x where x represents the last position -1.
Decimal Number System
The number system that we use
in our day-to- day life is the decimal number system. Decimal number system has
base 10 digits as it uses 10 digits from 0 to 9. In decimal number system, the
successive positions to the left of the decimal point represent units, tense,
hundred, thousands and so on. Each position represents a specific power of the
base (10). For example, the decimal number 1234 consists of the digit 4 in the
units position, 3 in the tense position, 2 in the hundreds position, and 1 in
the thousand position, and its value can be written as…
1x 1000) + (2x100) + (3x10) +
(4x1)
1x103) + (2x102)
+ (3x101) + (4x100)
1000 + 200 + 4
1234
Hexadecimal Number system
Hexadecimal Number system is a
number system which has base (radix) is 16 ranging from 0 to 9 and up to from A
to F means if write completely then it will be like this 0, 1, 2, 3, 4, 5, 6,
7, 8, 9, A, B, C, D, E, F, A number of Hexadecimal number system is written
like this (4A7)16 or 4A7 (hex.). Hexadecimal number is representing
always in 4 bits each.
Number System Conversion
here we see that
method and criteria converting a number system to another. We will be looking
forward to convert each into everyone. Here we see…
Binary to Decimal
We can convert a Binary number
to decimal. As we see binary number has base 2 whereas decimal number has base
10. The decimal of a binary number can be obtained when each binary number will
be multiplied with its positional value from the right. The first right binary
value has the positional value 20 and it will increase to 1 to the left
respectively.
For example:
(1001)2 =1*23+0*22+0*21+1*20
= 1*8+0*4+0*2+1*1
= 8+0+0+1
= 9
Hence the decimal of (1001)2
is 9.
Decimal to Binary
We can convert a decimal
number to binary number dividing the decimal number by the radix or base of the
binary number 2 repeatedly until you get the divination result whether 0 or 1
and we read or put remainder values in each divination in reverse order putting
a base 2 that is the binary number of that decimal number.
For e.g. binary of this decimal number (25)10=?
Read the remainder in reverse order to get the binary of this given decimal number. Hence the binary of (25)10= (11001)2
Hexadecimal to Decimal
We can convert a hexadecimal number to decimal. As we see decimal number has
base 10 whereas hexadecimal number has base 16. The decimal number of a
hexadecimal number can be obtained when each hexadecimal number will be
multiplied with its positional value from the right. The first right binary
value has the positional value 160 and it will increase to the left
respectively.
For example:
(4A7)16
= 4*162+A*161+7*160
=
4*256+10*16+7*1
=
1024+160+7
= 1191
Hence
the decimal value of (4A7)16is Hexadecimal to Binary
As we studied earlier
that in a hexadecimal number each digit is represented by 4 bits so while
converting a hexadecimal number to binary we need to represent binary of each
digit of hexadecimal number in 4-4 bits.
Binary to Hexadecimal
Hexadecimal converting a binary to
hexadecimal we need to divide 4-4 bits value group in given binary number them
find the hexadecimal of divide binary values with the predefined procedure.
Hence binary of (4A7)16 is (01001010111)
Octal to Binary
Here we see
some simple step doing this possible…
Steps 1 – Convert the
original number to a decimal number (base 10).
Steps 2 - Convert the
decimal number so obtained to the new base number.
For example (25)8
Converting this number to decimal first…
|
|
Now converting the gotten number to binary…
For this as we have already discussed diking early
topics that a decimal number will be converted into the binary one by dividing
by nits radix which is 2, and we put the remainders in reverse order. By doing
that we get:
(21)10 = (10101)2
Then we see that (25)8 = (10101)2
Binary to octal: Here we see
some simple step doing this possible…
Step 1 – Divide the
binary digits into groups of three (starting from the right).
Step 2 – Convert each
group of three binary digits to one decimal digit.
Step 3 – Now
substitute all decimal digit into one; that will be your octal digit equivalent
to that binary.
Consider (10101)2
Step
|
Binary
|
Octal Number
|
Step 1
|
(10101)
|
(010) (101)
|
Step 2
|
(10101)
|
2 5
|
Step 3
|
(10101)2
|
(25)8
|
So, (10101)2 = (25)8
CONCEPT OF DATA PROCESSING
Computerized data processing or Electronic data processing represents the further evolution, with the computer taking the place of several independent pieces of equipment. Data Processing is subject matter of taking data or information as input and processing the data and letting you have the output result.
Data/ Information
This is the
raw fact or information which is considered as input for a certain task to take
place.
Processing: It is the
intermediate operation which does over all operation on the data or information
to have the desired output result.
Output: It is the last step in which a user is availed the
result output.
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