# Chapter No.5 DATA REPRESENTATION

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1 Chapter No.5 DATA REPRESENTATION Q.5.01 Complete the following statements. i) Data is a collection of ii) Data becomes information when properly. iii) Octal equivalent of binary number is iv) 2 s complement of binary number is v) In floating point representation, mantises is kept less than vi) ASCII stands for i) raw facts ii) arranged iii) 142 iv) v) 1 iv) American Standard Code for Information Interchange Q.5.02 Which of the following statements are True or False? i) PK 345 is an example of Alphabetic data. ii) 128 is not an octal number. iii) In hexadecimal number F is equivalent to 16 in decimal number. iv) EBCDIC code is used in IBM compatible computers. v) Binary Coded Decimal (BCD) is a 10-bit code. i) False ii) True iii) False iv) True v) False Q.5.03 Encircle one Choice A, B, C or D I each case i) Binary coded decimal (BCD) express each decimal digit as: (A) Binary digit (B) Byte (C) Nibble (D) Word ii) The number 1000 comes immediately after: (A) 900 (B) FFF (C) 887 (D) 499 iii) The radix of a computerized version of the number (+0.66 E 4) is: (A) 2 (B) 4 (C) 6 (D) 8 iv) The number of possible combinations in a 7-bit code are: (A) 49 (B) 64 (C) 128 (D) 256 v) Which of the following is a 16-bit code? (A) BCD (B) Unicode (C) ASCII (D) EBCDIC i) (A) ii) (C) iii) (A) iv) (C) v) (B) 1

2 Q.5.04 Match the items given in Column I with those given in Column II Column I Column II i) Mantissa a) Nibble ii) Radix b) Byte iii) Exponent c) Argument iv) BCD d) Base v) ASCII e) Characteristics i) (c) ii) (d) iii) (e) iv) (a) v) (b) Q.5.06 Describe the importance of binary number system in computers. The importance of binary numbers in standard computing is basically everything. Computers only understand base 2 that is a 0 (off) and a 1 (on). Every piece of data passed through any part of the computer is done so using base 2 (binary). Q.5.07 Convert the following decimal numbers into their binary equivalent. (i) 47 (ii) 167 (iii) (iv) Example: Convert Decimal number into Binary equivalent X 2 = X 2 = Hence (25.75) 10 = ( ) 2 Q.5.08 Convert the following binary numbers into their decimal equivalent. (i) (ii) (iii) (iv)

3 Example: Convert Binary number into decimal equivalent. ( ) 2 = 1 X X X X X X X X 2-3 = 1 X X X X X = = = = (22.625) 10 Q.5.09 Convert the following decimal numbers into their octal equivalent. (i) 43 (ii) 291 (iii) 168 (iv) 2101 Example: Convert Decimal number 1583 into Octal equivalent Hence (1583) 10 = (3057) 8 Q.5.10 Convert the following octal numbers into their decimal equivalent. (i) 27 (iii) 372 (iii) 1101 (iv) 2345 Example: Convert octal number 3057 into decimal equivalent. 3

4 (3057) 8 = 3 X X X X 8 0 = 3 X X X X 1 = = 1583 = (1583) 10 Q.5.11 Convert the following decimal numbers into their Hexadecimal equivalent. (i) 37 (iii) 141 (iii) 532 (iv) 702 Example: Convert Decimal number into Hexadecimal equivalent =A =B 4 =E Hence (20154) 10 = (4EBA) 16 Q.5.12 Convert the following Hexadecimal numbers into their decimal equivalent. (i) 4F (iii) BA4C (iii) 532 (iv) 702 Example: Convert Hexadecimal number 3F8A into decimal equivalent. (3F8A) 16 = 3 X F X X A X 16 0 = 3 X X X X 1 = = = (16266) 10 4

5 Q.5.13 Subtract: (i) from (ii) from (iii) from (iv) from (v) from using 1 s and 2 s complement for part (i) to (iv) Above questions from (i) to (iv) are same as the following example. Example: part (v) is same as the following example: Example: Subtract (1101) 2 from (10010) 2 in binary system using 1 s and 2 s complement method. 1 s Complement Method: 1 st make equal digits in both the numbers by adding 0 s on the left. Like following Making equal digits of Binary numbers: and s complement of = Adding 1 s complement of Adding the carry Thus (10010) 2 (1101) 2 = (101) 2 2 s Complement Method: 1 st make equal digits in both the numbers by adding 0 s on the left. Like following 5

6 Making equal digits of Binary numbers: and s complement of = s complement of = = Adding 2 s complement of Dropping the carry Thus (10010) 2 (1101) 2 = (101) 2 Q.5.14 What is meant by coding in computers? Coding is the process of representing all the numeric or non-numeric information in binary digits. The language of electronic computers is binary therefore all the numeric or non-numeric data must be converted in to binary language. Q.5.15 Describe ASCII code and EBCDIC code? The ASCII Code ASCII stands for American Standard Code for Information Interchange. It is 7-bit code used to handle alphanumeric data having 128 different characters. It is the most popular coding system for PC s and data communication. This code allows manufactures to standardize input/output devices such as keyboard, printers visual display unit etc. The EBCDIC Code EBCDIC stands for Extended Binary Coded Decimal Interchange Code. It an 8-bit code and can provide 256 different characters. It is primarily used by International Business Machine on IBM mainframes and on other large computers. 6

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