030010105: Mathematics for Computer Application 2014

Mr. Nikhil Choksi Page 1

B.C.A.(1st Semester)030010105: Mathematics for Computer Applications

Unit 1: Data Representation & Binary MathematicsShort Answer Questions:

1. Why computer system is known as two state devices?2. Why binary digits are used to store the data in a computer?3. Under what circumstances are decimal digits coded using ASCII?4. List two different ways to store negative number in computer system.5. Give one example in which ASCII code is assigned to decimal digits.6. Decode the following ASCII message.

1010011101010010101011000100101100101000001001000100000110100101000100

7. Give atleast two example where hexadecimal number system is more preferable as compare toother number system.

8. How many unique strings are there with 6 bits in each string?9. How many bits per character does ASCII code and ISCII use?10. If the capital English letters, digits and 16 special characters are to be coded as strings of

bits, how many bits will be required for each string?11. What are the decimal equivalents of the following binary fractions?

(a)0.01101 (b)1111011.101 (c) 11000.001112. What is the decimal equivalent of the octal fraction 120.647?13. What are the binary equivalents of the following decimal fractions?

(a) 0.7625 (b) 25.25 (c) 27.187514. Convert the following binary numbers into its hexadecimal values:

(a)100101.010101 (b) 01011.1011101 (c) 10110000.0115. Convert the following decimal numbers to hexadecimal equivalents:

(a)285.48 (b) 3452.645 (c) 678920.45 (d)10000.0039062516. Convert the following hexadecimal numbers to their decimal equivalents:

(a) F.4 (b) D3.E (c) 1111.1 (d) EBA.C17. Find the Binary Sums:

(a)1101+111 (b) 110011+11101 (c) 110.1101+1011.101(d)1110.1101 + 110101.01101 (e) 11001 +11100 + 1011 + 110011

18. Find the Binary products:(a)11100111 x 11 (b) 111011 x 1011 (c) 11.101 x 11.01(d) 110.101 x 1011.001 (e) 1101.101 x 110101.11

19. Find the Binary differences:(a)1100011-110111 (b) 10101010-110011 (c) 110.001-11.111(d) 10101.1010 – 10001.0011 (e) 11011.011 - 11110.101(f) 1001000.001 – 1000011.011

20. Find the quotients:(a) 1011011 /111 (b) 100.0001 /10.1 (c) 1011 /11

(d)1011/011 (e) 110111/1011 (f) 110001.110/111.110

Long Answer Questions:

030010105: Mathematics for Computer Application 2014

Mr. Nikhil Choksi Page 2

1. We can implement hexadecimal number system instead of binary number system in computer.Justify your answer.

2. What is Unicode? What is the advantage of using Unicode?3. Under what circumstances are decimal numbers converted into binary numbers?4. What is the difference between the bits used in a code such as ASCII and the bits used in binary

numbers?5. What is the advantage of using hexadecimal numbers?6. Define the base of a number system and state the radix of the Decimal, Binary and Hexadecimal

number systems.7. Explain the terms “External representation” and the “Internal representation” of data in a

Computer.8. What are the different character representation are available in binary number system? Which

character representation is best in which condition?9. What are the considerations that govern the selection of a representation for storing and

processing data in a computer?10. How many average binary digits are required to represent a decimal digit? Explain in detail.11. Which number system is better to represent negative real number binary number system

between signed magnitude and 2’s complement? Justify your answer.12. Explain the normalized floating point mode of representing and storing real numbers.13. Subtract the following binary numbers using 2’s complement representation of negative

numbers:(a)10101-10001 (b) 11011-1110 (c) 100100-100011

14. Convert the following binary numbers to their decimal equivalents:(a)1001.1111 (b) 110101.011001 (c) 10100111.111011

15. Subtract the following binary numbers using 2numbers:(a)101101.0011-100101.0001 (b) 11011.110-101.001 (c) 10111.1001-11000.1101

16. Add the following binary numbers using 16-bit floating point representation:(a)1011011.110101 + 110101.0101 (b) 11011.1101 + 1011.10110(c)0.000111 + 111.00111

17. Subtract the following binary numbers using a 16-bit floating point representation:(a)1011011.1101 – 01110.1101 (b) 101110.110 – 1110.0011 (c)100110.101 – 011.110011

18. Multiply the following numbers using a 16-bit floating point representation:(a)1011.110 x 1010.110 (b) 0.11011 x 11011.1101 (c)1110111.111 x 11011.1101

19. Divide the following numbers using a 16-bit floating point representation:(a)1011.110 / 1010.110 (b) 0.11011 / 0.111011 (c) 110111.111 / 11011.1101

Select correct option from given choice1. Why the decimal number system is also called as positional number system?

a. Since the values of the numbers are decided by multiplying the values.b. Since the values of the numbers are decided by the weight of the values.c. Since the values of the numbers are decided by adding the values.d. Since the values of the numbers are decided by the position of the values.

2. How can you represent a decimal point?a. By a series of coefficients.b. By weight decided by its position.

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c. By location as well as based. None of the above

3. A digit in base R will have a range from ____________.a. 1 to R-1b. 0 to R-1c. 1 to R+1d. 0 to R+1

4.Conversion from any base to decimal base is done by ___________ each digit by itscorresponding weight and then ___________ all the individual products to get theequivalent decimal value.a. Multiplying, Addingb. Adding, Multiplyingc. Dividing, Addingd. Adding, Subtracting

5. Which method is used to convert a number from an octal base to decimal base?a. Direct conversion methodb. Decimal equivalent methodc. Octal equivalent methodd. Positional notation method

6. In which conversion the product of number 16 raised by the location and then adds all theproducts to get the final decimal value?a. Octal to decimalb. Binary to Decimalc. Hexadecimal to decimald. None of the above

7. Binary numbers can be converted into equivalent octal numbers by making groupsof threebits _____________.a. Starting from the MSBb. Starting from the LSBc. Ending at the MSBd. Ending at the LSB

8. In direct conversion from binary to hexadecimal, if the last group does not have 4-bits,then it is padded with ______________ to make it four bits.a. Zerosb. Onesc. Two zeros and two onesd. One zero and three ones

9. The sign information has to be encoded along with the ___________ to represent theintegers completely.a. No. of bitsb. Positionc. Magnituded. Weight

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10. Which one is the possible technique for representing signed integers?a. Signed Magnitude Representationb. Diminished Radix-Complement Representationc. Radix-Complement Representationd. All of the above

11. What is used to represent the signed magnitude?a. MSBb. LSBc. Bothd. None of the above

12. What is the corresponding hex number of the signed magnitude -127?a. (7F)16

b. (FF)16

c. (00)16

d. (80)16

13. (FA)16 is the ________ one’s complement representation of -5.a. 4-bitb. 8-bitc. 16-bitd. 2-bit

14. 2’s complement is used to represent signed integers, especially __________ integers.a. Negativeb. Positivec. Both A and Bd. None of the above