**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 2
^{7}= 128 (from 0 to 127) unique symbols. - ASCII-8 It is a extended version of ASCII-7. It is an 8-bit code, allows 2
^{8}= 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 2^{8} = 256 combinations of bits.

**QUESTION BANK**

**1. A hexadecimal number is represented by**

- three digits
- four binary digits
- four digits
- All of these
- None of these

**2. Decimal number system is the group of**

- 0 or 1
- 0 to 9
- 0 to 7
- 0 to 9 and A to F
- None of these

**3. Hexadecimal number system has ……….**

- 2
- 8
- 10
- 16
- None of these

**4. Hexadecimal number system consists of**

- 0 to 9
- A to F
- Both ‘1’ and ‘2’
- Either ‘1’ or ‘2’
- Neither ‘1’ nor ‘2’

**5. Which of the following statements is true?**

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

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

- binary system
- barter system
- number system
- hexadecimal system
- special system

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

- 3
- 5
- 6
- 101
- 7

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

- 12
- 65
- 56
- 1111
- 00

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

- 9F
- FF
- 99
- F9
- FC

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

- (100011001)
_{2} - (.100011001)
_{2} - (100110100)
_{2} - (.100110001)
_{2} - (1000.11001)
_{2}

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

- 0061
- 6001
- 1006
- 1600
- 0601

**12. Which of the following is invalid hexadecimal number?**

- A0XB
- A0F6
- 4568
- ACDB
- 60AC

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

- 197
- 917
- 791
- 971
- 719

**14. There are how many types of number system?**

- One
- Two
- Three
- Four
- Five

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

- 4
- 16
- 64
- 256
- 512

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

- Penta
- Octal
- Hexa
- Septa
- Binary

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

- EBCDIC
- ASCII
- CISC
- UNICODE
- None of these

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

- ASCII
- UNICODE
- EBCDIC
- All of these
- None of these

**19. MSD refers as**

- Most Significant Digit
- Many Significant Digit
- Multiple Significant Digit
- Most Significant Decimal
- None of the above

**20. Binary system is also called**

- base one system
- base two system
- base system
- binary system
- None of these

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

- Sign magnitude
- 1’s compliment
- 2’s compliment
- All of these
- None of these

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

- ASCII
- EBCDIC
- BCD
- Both ‘1’ and ‘2’
- All of these

**23. (1010) _{2} equivalent decimal number is**

- 8
- 9
- 10
- 11
- 12

**24. The digits of the binary system are called**

- bytes
- bits
- nibbles
- number
- None of these

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

- binary
- biometric
- bicentennial
- byte
- None of these

**26. Conversion of decimal number (42) _{10} to its octal number equivalent is**

- (57)
_{8} - (42)
_{8} - (47)
_{8} - (52)
_{8} - None of these

**27. Most commonly used codes for representing bits are**

- ASCII
- BCD
- EBCDIC
- All of these
- None of these

**28. Determine the octal equivalent of (432267 ) _{10}**

- (432267 )
_{8} - (346731)
_{8} - (2164432)
_{8} - (123401)
_{8} - None of these

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

- digit is divided by-8
- digit is multiplied by the corresponding power of 8
- digit is added with-8
- digit is subtracted with-8
- None of the above

**30. Conversion of decimal number (99) _{10} to its binary number equivalent is**

- (1100011)
_{2} - (100011)
_{2} - (1110001)
_{2} - (1111000)
_{2} - None of these

**31. Conversion of octal number(3137) _{8} to its decimal equivalent is**

- (1631)
_{10} - (1632)
_{10} - (1531)
_{10} - (1931)
_{10} - None of these

**32. LSD stands for**

- Long Significant Digit
- Least Significant Digit
- Large Significant Digit
- Longer Significant Decimal
- None of the above

**33. Determine the decimal equivalent of (456) _{8}**

- (203)
_{10} - (302)
_{10} - (400)
_{10} - (402)
_{10 } - None of these

**34. Conversion of decimal number (93) _{10} to hexadecimal number is**

- (2D)
_{16} - (5D)
_{16} - (62)
_{16} - (31)
_{16} - None of these

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

- decimal number
- whole number
- hexadecimal number
- exponential integers
- Mantissa

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

- 0
- 2
- 4
- 6
- 8

**37. Conversion of decimal number (15) _{10} to hexadecimal number is**

- (14)
_{16} - (13)
_{16} - (F)
_{16} - (7F)
_{16} - (FF
_{6})

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

- Extension of BCD information code
- Extended of BCD interchange code
- Extension of BCD interchange conduct
- Extended BCD information conduct
- None of the above

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

- 356
- 756
- 556
- 256
- 156

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

- decimal
- hexadecimal
- octal
- binary
- 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**

- 8 bytes
- 8 KB
- 8 character
- 8 bits
- None of these

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

- Hexadecimal system
- Binary system
- Both ‘1’ and ‘2’
- Only roman system
- None of the above

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

- 6AH1
- 100101
- 005
- ABCD
- 23456

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

- 001
- 101
- 202
- 110
- 011

**45. The octal system [IBPS Clerk 2011]**

- needs less digits to represent a number than in the binary system
- needs more digits to represent a number than in the binary system
- needs the same number of digits to represent a number as in the binary system
- needs the same number of digits to represent a number as in the decimal system
- None of the above

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

- ASCII
- UNICODE
- BCD
- EBCDIC
- None of these

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

- (40)
_{15} - (39)
_{16} - (49)
_{16} - (42)
_{16} - None of these

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

- (35)
_{16} - (46)
_{16} - (2E )
_{16} - (50)
_{16} - None of these

**49. Decimal equivalent of (1111) _{2} is [IBPS Clerk 2012]**

- 11
- 10
- 1
- 15
- 13

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

- 1110001
- 1110100
- 1100010
- 1111001
- None of these

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

- three binary (consecutive) bits
- four binary (consecutive) bits
- eight binary (consecutive) bits
- sixteen binary (consecutive) bits
- None of the above

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

- (110011)
_{2} - (1110011)
_{2} - (0110011)
_{2} - (1000111)
_{2} - None of these

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

- (110011)
_{2} - (11001110)
_{2} - (111101)
_{2} - (11111)
_{2} - None of these

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

- binary
- octal
- decimal
- hexadecimal
- None of these

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

- American Special Computer for Information Interaction
- American Standard Computer for Information Interchange
- American Special Code for Information Interchange
- American Special Computer for Information Interchange
- American Standard Code for Information Interchange

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

- instructor
- decoder
- AND gate
- converter
- decoder

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

- 11101
- 110
- 233
- 1001
- 100110

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

- 36
- 10
- 45
- 29
- 12

**ANSWERS**

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