Computer Awareness Study Material – Data Representation

Computer Awareness Study Material – Data Representation

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Data representation refers those methods which are used internally to represent information stored in a computer. Computers store lots of different types of information as numbers, text, graphics, sounds, etc.

Number System
It defines a set of values that is used to represent quantity. Digital computers internally use the binary number system to represent data and perform arithmetic calculations.

Types of Number System
The number systems generally used by a computer are as follows
Binary Number System
This system is very efficient for computers, but not for humans. It contains only two unique digits 0’s and l’s. It is also known as Base 2 system. The binary numbers 0 and 1 are called a bit. The computer always calculates input in binary form. e.g. (10101)₂
Here, 2 represents base of binary number.

Decimal Number System
It consists of 10 digits from 0 to 9. These digits can be used to represent any numeric value. It is also known as Base 10 system or positional number system, e.g. (1275)₁₀,(10406)₁₀

Octal Number System
It consists of 8 digits from 0 to 7. It is also known as Base 8 system. Each position of the octal number represents a successive power of eight.

Hexadecimal Number System
It provides us with a shorthand method of working with binary numbers. There are 16 unique digits available in this system.
These are 0 to 9 and A to F, where A denotes 10, B denotes 11……. F denotes 15. It is also known as Base 16 system or simply Hex. So, each position of the hexadecimal number represents a successive power of 16.

Conversion between the Number Systems
Different types of conversion between the number systems are discussed below

Decimal to Binary
To convert decimal to binary following steps are involved
Step 1 – Divide the given number by 2.
Step 2 – Note the quotient and remainder. Remainder should be 0 or 1.
Step 3 – If quotient 0, then again divide the quotient by 2 and back to step 2.
If quotient = 0, then stop the process.
Step 4 – First remainder is called as Least
Significant Bit (LSB) and last remainder is called as Most Significant Bit (MSB).
Step 5 – Arrange all remainders from MSB to LSB.

Binary to Decimal
To convert binary to decimal following steps are involved
Step 1 – Multiply the all binary digits by powers of 2.
Step 2 – The power for integral part will be positive and for fractional part will be negative.
Step 3 – Add the all multiplying digits.

Binary to Octal
To convert binary to octal following steps are involved
Step 1 – Make the group of 3 bits from right to left. If the left most group has less than 3 bits, put in the necessary number of leading zeroes on the left.
Step 2 – Now, convert each group to decimal number.

Octal to Binary
Convert every digit of the number from octal to binary in the group of 3 bits.

Binary to Hexadecimal
To convert a binary number to its hexadecimal equivalent follow these steps
Step 1 – Start making the group of 4 bits each from right to left from the given binary number. If the left most group has less than 4 bits, put in the necessary number of leading 0’s on the left.
Step 2 – Now, each group will be converted to decimal number.

Hexadecimal to Binary

For this type of conversion, convert each hexadecimal digit to 4 bits binary equivalent.

Decimal to Octal
To convert decimal to octal following steps are involved
Step 1 – Divide the given number by 8.
Step 2 – Note the quotient and remainder. Digits of remainder will be from 0 to 7.
Step 3 – If quotient 0, then again divide the quotient by 8 and go back to step 2.
Step 4 – If quotient = 0, then stop the process.
Step 5 – Write each remainder from left to right starting from MSD to LSD.

Octal to Decimal
To convert octal to decimal following steps are involves
Step 1 – Multiply each digit of octal number with powers of 8.
Step 2 – These powers should be positive for integral part and negative for fractional part.
Step 3 – Add the all multiplying digits.

Decimal to Hexadecimal
To convert decimal to hexadecimal, following steps are involves
Step 1 – Divide the given number by 16.
Step 2 – Note the quotient and remainder. Digits of remainder will be 0 to 9 or A to F.
Step 3 – If quotient 0, then again divide the quotient by 16 and go back to step 2.
Step 4 – If quotient = 0 or less than 16, then stop the process.

Hexadecimal to Decimal
To convert hexadecimal to decimal following steps are involved
Step 1 – Multiply each digit of hexadecimal number with powers of 16.
Step 2 – These powers should be positive for integral part and negative for fractional part.
Step 3 – Add the all multiplying digits.

Computer Codes
In computer, any characters like alphabet, digit or any special character is represented by collection of l’s and 0’s in a unique coded pattern. In computers, the code is made up of fixed size groups of binary positions. The binary coding schemes that are most commonly used are as follows

Binary Coded Decimal (BCD)
It is a number system where four bits are used to represent each decimal digits. BCD is a method of using binary digits to represent the decimal digits (0-9). In BCD system, there is no limit on size of a number.

American Standard Code for Information Interchange (ASCII)
These are standard character codes used to store data so that it may be used by other software programs. Basically, ASCII codes are of two types which as follows

• ASCII-7 It is a 7-bit standard ASCII code. It allows 2⁷ = 128 (from 0 to 127) unique symbols.
• ASCII-8 It is a extended version of ASCII-7. It is an 8-bit code, allows 2⁸ = 256 (0 to 255) unique symbols or characters.

Extended Binary Coded Decimal Interchange Code (EBCDIC)
In EBCDIC, characters are represented by eight bits. These codes store information which is readable by other computers. It allows 2⁸ = 256 combinations of bits.

QUESTION BANK

1. A hexadecimal number is represented by

1. three digits
2. four binary digits
3. four digits
4. All of these
5. None of these

2. Decimal number system is the group of

1. 0 or 1
2. 0 to 9
3. 0 to 7
4. 0 to 9 and A to F
5. None of these

3. Hexadecimal number system has ……….

1. 2
2. 8
3. 10
4. 16
5. None of these

4. Hexadecimal number system consists of

1. 0 to 9
2. A to F
3. Both ‘1’ and ‘2’
4. Either ‘1’ or ‘2’
5. Neither ‘1’ nor ‘2’

5. Which of the following statements is true?

1. 1 gigabyte is equivalent to 1024 kilobyte
2. Mb stands for megabyte
3. Octal number system having 8 digits
4. Decimal number system cannot contain binary digits
5. None of the above

6. The number system based on ‘0’ and ‘1′ only, is known as

1. binary system
2. barter system
3. number system
4. hexadecimal system
5. special system

7. What is the value of the binary number 101?

1. 3
2. 5
3. 6
4. 101
5. 7

8. Which of the following is octal number equivalent to binary number (110101)₂ ?

1. 12
2. 65
3. 56
4. 1111
5. 00

9. Which of the following is hexadecimal number equivalent to binary number (1111 1001 )₂?

1. 9F
2. FF
3. 99
4. F9
5. FC

10. Which of the following is a binary number equivalent to octal number (.431)₂?

1. (100011001)₂
2. (.100011001)₂
3. (100110100)₂
4. (.100110001)₂
5. (1000.11001)₂

11. Which of the following is an octal number equal to decimal number (896)₁₀?

1. 0061
2. 6001
3. 1006
4. 1600
5. 0601

12. Which of the following is invalid hexadecimal number?

1. A0XB
2. A0F6
3. 4568
4. ACDB
5. 60AC

13. Which of the following is a hexadecimal number equal to 3431 octal number?

1. 197
2. 917
3. 791
4. 971
5. 719

14. There are how many types of number system?

1. One
2. Two
3. Three
4. Four
5. Five

15. How many values can be represented by a single byte?

1. 4
2. 16
3. 64
4. 256
5. 512

16. Modern computers represent characters and numbers internally using one of the following number systems.

1. Penta
2. Octal
3. Hexa
4. Septa
5. Binary

17. Which of the following is not a computer code?

1. EBCDIC
2. ASCII
3. CISC
4. UNICODE
5. None of these

18. The coding system allows non-english characters and special characters to be represented

1. ASCII
2. UNICODE
3. EBCDIC
4. All of these
5. None of these

19. MSD refers as

1. Most Significant Digit
2. Many Significant Digit
3. Multiple Significant Digit
4. Most Significant Decimal
5. None of the above

20. Binary system is also called

1. base one system
2. base two system
3. base system
4. binary system
5. None of these

21. The negative numbers in the binary system can be represented by

1. Sign magnitude
2. 1’s compliment
3. 2’s compliment
4. All of these
5. None of these

22. Today’s mostly used coding system is/are

1. ASCII
2. EBCDIC
3. BCD
4. Both ‘1’ and ‘2’
5. All of these

23. (1010)₂ equivalent decimal number is

1. 8
2. 9
3. 10
4. 11
5. 12

24. The digits of the binary system are called

1. bytes
2. bits
3. nibbles
4. number
5. None of these

25. Data representation is based on the……….. number system, which uses two numbers to represent all data.

1. binary
2. biometric
3. bicentennial
4. byte
5. None of these

26. Conversion of decimal number (42)₁₀ to its octal number equivalent is

1. (57)₈
2. (42)₈
3. (47)₈
4. (52)₈
5. None of these

27. Most commonly used codes for representing bits are

1. ASCII
2. BCD
3. EBCDIC
4. All of these
5. None of these

28. Determine the octal equivalent of (432267 )₁₀

1. (432267 )₈
2. (346731)₈
3. (2164432)₈
4. (123401)₈
5. None of these

29. The method used for the conversion of octal to decimal fraction is

1. digit is divided by-8
2. digit is multiplied by the corresponding power of 8
3. digit is added with-8
4. digit is subtracted with-8
5. None of the above

30. Conversion of decimal number (99)₁₀ to its binary number equivalent is

1. (1100011)₂
2. (100011)₂
3. (1110001)₂
4. (1111000)₂
5. None of these

31. Conversion of octal number(3137)₈ to its decimal equivalent is

1. (1631)₁₀
2. (1632)₁₀
3. (1531)₁₀
4. (1931)₁₀
5. None of these

32. LSD stands for

1. Long Significant Digit
2. Least Significant Digit
3. Large Significant Digit
4. Longer Significant Decimal
5. None of the above

33. Determine the decimal equivalent of (456)₈

1. (203)₁₀
2. (302)₁₀
3. (400)₁₀
4. (402)₁₀
5. None of these

34. Conversion of decimal number (93)₁₀ to hexadecimal number is

1. (2D)₁₆
2. (5D)₁₆
3. (62)₁₆
4. (31)₁₆
5. None of these

35. Numbers that are written with base 10 are classified as

1. decimal number
2. whole number
3. hexadecimal number
4. exponential integers
5. Mantissa

36. To convert binary number to decimal, multiply the all binary digits by power of

1. 0
2. 2
3. 4
4. 6
5. 8

37. Conversion of decimal number (15)₁₀ to hexadecimal number is

1. (14)₁₆
2. (13)₁₆
3. (F)₁₆
4. (7F)₁₆
5. (FF₆)

38. Code ‘EBCDIC’ that is used in computing stands for

1. Extension of BCD information code
2. Extended of BCD interchange code
3. Extension of BCD interchange conduct
4. Extended BCD information conduct
5. None of the above

39. In EBCDIC code, maximum possible characters set size is

1. 356
2. 756
3. 556
4. 256
5. 156

40. To perform calculation on stored data computer uses……………. number system.

1. decimal
2. hexadecimal
3. octal
4. binary
5. None of these

41. In the binary language, each letter of the alphabet, each number and each special character is made up of a unique combination of

1. 8 bytes
2. 8 KB
3. 8 character
4. 8 bits
5. None of these

42. What type of information system would be recognized by digital circuits?

1. Hexadecimal system
2. Binary system
3. Both ‘1’ and ‘2’
4. Only roman system
5. None of the above

43. Which of the following is an example of binary number?                          [IBPS Clerk 2011]

1. 6AH1
2. 100101
3. 005
4. ABCD
5. 23456

44. Which of the following is not a binary number?                              [IBPS Clerk 2011]

1. 001
2. 101
3. 202
4. 110
5. 011

45. The octal system [IBPS Clerk 2011]

1. needs less digits to represent a number than in the binary system
2. needs more digits to represent a number than in the binary system
3. needs the same number of digits to represent a number as in the binary system
4. needs the same number of digits to represent a number as in the decimal system
5. None of the above

46.The most widely used code that represents each character as a unique 8-bit code is [IBPS Clerk 2011]

1. ASCII
2. UNICODE
3. BCD
4. EBCDIC
5. None of these

47. Conversion of binary number (1001001)₂ to hexadecimal is                             [SBI PO 2011]

1. (40)₁₅
2. (39)₁₆
3. (49)₁₆
4. (42)₁₆
5. None of these

48. Conversion of binary number (101110)₂ to hexadecimal is                             [SBI PO 2011]

1. (35)₁₆
2. (46)₁₆
3. (2E )₁₆
4. (50)₁₆
5. None of these

49. Decimal equivalent of (1111)₂ is  [IBPS Clerk 2012]

1. 11
2. 10
3. 1
4. 15
5. 13

50. The binary equivalent of decimal number 98 is                                            [IBPS Clerk 2012]

1. 1110001
2. 1110100
3. 1100010
4. 1111001
5. None of these

51. A hexadigit can be represented by  [IBPS Clerk 2012]

1. three binary (consecutive) bits
2. four binary (consecutive) bits
3. eight binary (consecutive) bits
4. sixteen binary (consecutive) bits
5. None of the above

52. Conversion of decimal number (71)₁₀ to its binary number equivalent is [IBPS Clerk 2012]

1. (110011)₂
2. (1110011)₂
3. (0110011)₂
4. (1000111)₂
5. None of these

53. Conversion of decimal number (61)₁₀ to its binary number equivalent is [IBPS Clerk 2012]

1. (110011)₂
2. (11001110)₂
3. (111101)₂
4. (11111)₂
5. None of these

54. Computer uses the……………. number system to store data and perform calculations [IBPS Clerk 2013]

1. binary
2. octal
3. decimal
4. hexadecimal
5. None of these

55. ASCH stands for [IBPS Clerk 2011,2014]

1. American Special Computer for Information Interaction
2. American Standard Computer for Information Interchange
3. American Special Code for Information Interchange
4. American Special Computer for Information Interchange
5. American Standard Code for Information Interchange

56. A device that converts from decimal to binary number is known as  [IBPS Clerk 2014]

1. instructor
2. decoder
3. AND gate
4. converter
5. decoder

57. Which of the following is not a binary number?        [IBPS Clerk 2014]

1. 11101
2. 110
3. 233
4. 1001
5. 100110

58. Which of the following is a binary number ? [SBI Clerk 2014]

1. 36
2. 10
3. 45
4. 29
5. 12

ANSWERS