1) A computer manipulates data by storing, retrieving, and processing it. Machine code, consisting of binary numbers, is the lowest-level language directly understood by computers. 2) There are four main number systems for representing data in computers: decimal, binary, octal, and hexadecimal. Each has a different base - 10 for decimal, 2 for binary, 8 for octal, 16 for hexadecimal. 3) Converting a decimal number to another base involves repeatedly dividing the number by the new base's value and recording the remainders as the new number in that base. For example, converting 17 to binary is (10001)2.

1. DATA REPRESENTATION
CLASS : XI
COMPUTER SCIENCE(083) - PYTHON
https://computerassignmentsforu.com

2. A computer is an electronic device that manipulates information, or data. It
has the ability to store, retrieve, and process data.
Machine language, or machine code, consists of binary code and is the only language
that is directly understood by the computer.
Which language is understood by the computer?
1010101010 These are the binary numbers that machine understand.
1
0
ON
OFF
TRUE
FALSE
BIT

3. What is Number System?
The technique to represent numbers in the computer system. When the data is
entered in a computer, it is converted into numeric format according to
ASCII(American Standard code for Information Interchange). In the number system,
each number is represented by its base number.
The number system classified into four fundamental types:
DECIMAL NUMBER SYSTEM
BINARY NUMBER SYSTEM
OCTAL NUMBER SYSTEM
HEXADECIMAL NUMBER SYSTEM

4. DECIMAL NUMBER SYSTEM:
In the decimal number system, the numbers are represented with base 10 means
digits from 0 to 9 only(0,1,2,3,4,5,6,7,8,9). The way of denoting the decimal numbers
with base 10 is also termed as decimal notation. Each digit has a value based on its
position called place value.
When we write numbers, the position (or "place") of each digit is important.
Example:
3 2 7 3 2 7
From Right To Left
As we move left, each position is 10 times bigger!

5. How we prove a DECIMAL NUMBER
Example:
(327)10
3 2 7
From Right To Left
7
2
3
x
x
x
10
10
10
=
=
=
0
1
2
7 x 1 = 7
2 x 10 = 20
3 x 100 = 300
Total: 327

6. Binary NUMBER SYSTEM:
In the Binary number system, the numbers are represented with base 2 means the
combination of 1 and 0.
Base Value is 2 (0,1)
Example:
( 1 0 1 1 1 ) 2
1 1 1
From Right To Left
01

7. octal NUMBER SYSTEM:
In the Octal number system, the numbers are represented with base 8 means digits
from 0 to 7 only(0,1,2,3,4,5,6,7).
Base Value is 8 (0 to 7)
Example:
( 2 4 6 ) 8
2 4 6
From Right To Left

8. hexadecimal NUMBER SYSTEM:
In the Hexadecimal number system, the numbers are represented
with base 16 means digits from 0 to 9.
Base Value is 16
Example: (A4C) 1 6
A 4 C
From Right To Left
As the base is greater than 9, the number system is supplemented by
letters.
10 =A 11 = B 12 = C 13 = D 14 = E 15 = F
10 4 12

9. Number System Conversion
TO CONVERT DECIMAL NUMBER TO BINARY NUMBER
TO CONVERT DECIMAL NUMBER TO OCTAL NUMBER
TO CONVERT DECIMAL NUMBER TO HEXADECIMAL NUMBER

10. CONVERT DECIMAL NUMBER TO BINARY NUMBER:
Let us take one decimal number first and then convert it to binary number:
(17)10 ( ? )2
=
In this case of converting decimal number to binary divide the
decimal number with the base value of binary number means
by 2.

11. CONVERT DECIMAL NUMBER TO BINARY NUMBER:
172
Remainder
8
1

12. CONVERT DECIMAL NUMBER TO BINARY NUMBER:
172
Remainder
8
1
2
4
0

13. CONVERT DECIMAL NUMBER TO BINARY NUMBER:
172
Remainder
8
1
2
4
0
2
2
0

14. CONVERT DECIMAL NUMBER TO BINARY NUMBER:
172
Remainder
8
1
2
4
0
2
2
0
2
1
0
(10001)2
(17)10 =
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15. CONVERT DECIMAL NUMBER TO OCTAL NUMBER:
Let us take one decimal number first and then convert it to OCTAL number:
(37)10 ( ? )8
=
In this case of converting decimal number to OCTAL divide the
decimal number with the base value of OCTAL number means
by 8.

16. CONVERT DECIMAL NUMBER TO OCTAL NUMBER:
378
Remainder
4
5
NEXT REMAIN 5 NOT DIVISIBLE BY 8
(37)10 ( 45 )8
=
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17. CONVERT DECIMAL NUMBER TO HEXADECIMAL NUMBER:
Let us take one decimal number first and then convert it to HEXADECIMAL number:
(125)10 ( ? )16
=
In this case of converting decimal number to HEXADECIMAL,
divide the decimal number with the base value of
HEXADECIMAL number means by 16.

18. CONVERT DECIMAL NUMBER TO HEXADECIMAL NUMBER:
12516
Remainder
7
13
NEXT REMAIN 7 NOT DIVISIBLE BY 16
(125)10 ( 713 )16= It is not the correct answer

19. CONVERT DECIMAL NUMBER TO HEXADECIMAL NUMBER:
(125)10 ( 713 )16=
So if the result is correct but WHY the
answer is still wrong.
7 D
Correct Answers is:
10 =A 11 = B 12 = C 13 = D 14 = E 15 = F
You know that in hexadecimal number base is 16 means number (0 to 9) , 10
,11,12,13,14,15 denoted by letters.
(125)10 ( 713 )16=
( 7D )16