## Kerala Plus One Computer Science Chapter Wise Questions and Answers Chapter 2 Data Representation and Boolean Algebra

**Very Short Answer Type Questions**

**(Score 1)**

Question 1.

Number of symbols used in a number system is called…………………..

Answer:

base

Question 2.

Pick invalid numbers from the following:

a. (10101)_{8}

b. (123)_{4 }c. (768)8

d. (ABC)_{16 }Answer:

c. (768)_{8}

Question 3.

Find MSD in the decimal number 7854.25

Answer:

7

Question 4.

The base of hexadecimal number system is……………….

Answer:

16

Question 5.

ASCII stands for…………………….

Answer:

American Standard Code for Information Interchange

Question 6.

A logic circuit is made up of individual units called

Answer:

gate

Question 7.

Name the logical operator/gate which gives high output if and only if all the inputs are high.

Answer:

AND gate

Question 8.

An AND operation performs logical and an OR operation performs logical………………

Answer:

Multiplication, addition

Question 9.

Name the law which states that A+A = A.

a. Commutative law

b. Idempotent Law

c. Absorption Law

d. Associative law

Answer:

b. Idempotent Law

Question 10.

……………… gate produces low (o) output if any one of the input is high (1)

a. OR

b. AND

c. NAND

d. NOR

Answer:

d. NOR

Question 11.

A NAND B = ………………….

a. A+B

b. A.B

c.

d.

Answer:

d.

Question 12.

JPEG stand for …………….

Answer:

Joint Picture Experts Group

Question 13.

C in hexadecimal number system is equivalent to………………. in binary number system,

a. 1001

b. 1010

c. 1011

d. 1100

Answer:

d. 1100

Question 14.

Define the term ‘bit’.

Answer:

Each digit of a binary number is called bit. A bit stands for binary digit.

Question 15.

Which is the MSB of representation of -80 in the sign and magnitude method?

Answer:

1

Question 16.

List any two image file formats.

Answer:

JPEG (Joint Picture Experts Group), bitmap file format (BMP), Tagged Image File Format (TIFF).

Question 17.

Define the term Boolean variable.

Answer:

The variables which can store (hold) logical constants 1 and 0 are known as boolean variables.

Question 18.

Define the term truth table.

Answer:

Truth table is a table that shows Boolean operations and their results. It lists all possible inputs for the given operation and their corresponding output.

Question 19.

Which gates are called universal gates?

Answer:

NAND and NOR gates

**Short Answer Type Questions**

**(Score 2)**

Question 1.

Find decimal equivalent of (1ooo1)_{2 }Answer:

1× 2^{4} + 0× 2^{3} + 0× 2^{2} + 0× 2^{1} + 1× 2°

= 16 + 0 + 0 + 0 + 1

= 17

(1ooo1)_{2} = (17)_{10}

Question 2.

If (x)_{8} = (1o1o11)_{2}, then find x.

Answer:

101 → 5, 011 → 3

x = 53

Question 3.

Define Unicode.

Answer:

Unicode is used to represent all characters of written languages of the world and other symbols. Unicode originally used 16 bits. It is maintained by a non-profit organisation called the Unicode Consortium.

Question 4.

Find the largest number in the list.

a. (1001)_{2}

b. (A)16

c. (10)_{8}

d. (11) _{10 }Answer:

The decimal conversion of all the numbers are 9, 10, 8 and 11. Then the largest is 11.

i.e, (11)_{10}

Question 5.

Draw the logic symbol of OR gate.

Answer:

Question 6.

Find the dual of Boolean expression A.B + B.C = 1

Answer:

A+B . B+C = 0

Question 7.

Define word length.

Answer:

A word is basically a fixed-sized group of bits that are handled as a unit by a processor. Number of bits in a word is called word length.

Question 8.

Write the following number in mantissa and exponent form.

a. 3718

b. -0.0035

Answer:

Any number in floating point notation contains two parts, mantissa and exponent.

a. 0.3718×10^{2 }Here 0.3718 is mantissa, 2 is exponent.

b. -0.0035 can be written as -0.35 × 10^{-2 }Here -0.35 is mantissa, -2 is exponent.

Question 9.

NOT gate is also known as inverter. Why?

Answer:

The input is always changed into its opposite state. If input is 0, the NOT gate will give its complement or opposite which is 1. If the input is 1, then the NOT gate will complement it to o.

Question 10.

Draw logic circuits for the Boolean expression X+Y .

Answer:

**Short Answer Type Questions**

**(Score 3)**

Question 1.

Convert the decimal number 31 to binary.

Answer:

Question 2.

Fill in the blanks:

a. (___________ )_{2} =(AB)_{16}

b. (____D____)_{16 }=(1010_____1000)_{2}

c. 0.2510=(___)_{2 }

Answer:

a.A → 1010, B →1011

(10101011)_{2}

b. (AD8)_{16}

=(1010 1101 1000)_{2}

c. (0.01)_{2}

Question 3.

State De Morgan’s theorems.

Answer:

- “The complement of sum of Boolean variables is equal to product of their individual complements”.

- “The complement of product of Boolean variables is equal to sum of their individual complements”.

Question 4.

What are the significance of octal and hexadecimal number system?

Answer:

Digital hardware uses the binary number system for its operations and data. Representing numbers and operations in binary form requires too many bits and needs lot of effort. With octal and hexadecimal, bits are grouped. These groups are replaced with the respective octal or hexadecimal symbol. This conversion processes of binary numbers to octal and hexadecimal number systems and vice versa are very easy

Question 5.

Convert 15.25 to binary.

Answer:

Question 6.

Draw a truth table for Idempotent law.

Answer:

This law states that, X + X = X and X . X = X

Question 7.

Construct a logical expression for

Answer:

Question 8.

How to implement below gates using NAND gate:

a. NOT gate

b. AND gate

c. OR gate

Answer:

Question 9.

How to implement below gates using NOR gate:

a. NOT gate

b. OR gate

c. AND gate

Answer:

**Long Answer Type Questions**

**(Score 5)**

Question 1.

Represent -60 in l’s complement form.

Answer:

1’s complement 11000011 -6o in 1’s complement form is 11000011

Question 2.

Write the proof of De Morgan’s theorem:

Answer:

**Textual Questions & Answers**

Question 1.

What is the place value of 9 in (296)_{10}? (1)

Answer:

10^{1}

Question 2.

Find octal equivalent of the decimal number 55. (2)

Answer:

Question 3.

Find missing terms in the following series. (2)

a. 101_{2} ,1010_{2}, 1111_{2},……………. ,…………..

b. 15_{8} ,16_{8}, 17_{8},…………………………………..

Answer:

a. 10100_{2}, 11001_{2}

b. 20_{g}, 21g

Question 4.

If (X)_{2} – (1010)_{2} = (1000)_{2} then find X. (2)

Answer:

(X)_{2} – (100)_{2} = (1000)_{2 }(X)_{2} – 10 = 8

18 – 10 = 8

(18)_{10} = (10010)_{2} = (X)_{2}

Question 5.

Name the coding system that can represent almost all the characters used in the human

languages in the world. (1)

Answer:

Unicode

Question 6.

List three basic logic gates. (x)

Answer:

OR gate, AND gate, NOT gate.

Question 7.

Which gate is called inverter? (x)

Answer:

NOT gate

Question 8.

List two complimentary Laws, (x)

Answer:

X + X = 1 and X . X = 0

Question 9.

The Boolean expression represents gate. (1)

a.AND

b. NOR

c. OR

d. NAND

Answer:

b. NOR

Question 10.

Define the term data representation. (1)

Answer:

Data representation is the method used internally to represent data in a computer.

Question 11.

What do you mean by a number system? List any four number systems. (2)

Answer:

Number system is a systematic way to represent numbers. Decimal, octal, binary and hexadecimal are the four types of number systems.

Question 12.

Convert the following number into the other three number systems: (125)_{g} (3)

Answer:

(125)_{8 }Binary system: 1 → 001, 2 → 010, 5 → 101

(125)3 = (001010101)_{2 }Decimal system: 1 × 8^{2} + 2 × 8^{1} +5 × 8°

= 64 + 16 + 5

= 85

(125)_{8} = (8_{5})_{10 }Hexadecimal system: Its binary is (oo1o1o1o1)_{2 }0000 → o, 0101 → 5, 0101 → 5 (125)_{8} = (55)_{16}

Question 13.

If (X)_{2} = (Y)_{8} = (Z)_{16} = (28)_{10} Then find X,Y and Z. (1)

Answer:

X = 11100, Y = 34, Z = 1C

Question 14.

Arrange the following numbers in descending order: (5)

a. (1o1)_{16} (no)_{10 }b. (10ooo)_{2} (251)_{8 }Answer:

Represent all the numbers in decimal form,

a. (101)_{16} = 1 × 16^{2} + o x 16^{1} + 1 ×16^{0 }= 256 + 0 + 1

= (257)_{10}_{ }b. (110)_{10 }c. (111000)_{2} = 1 ×2^{5} + 1 × 2^{4} + 1 × 2^{3 }+ O×2^{a} + O×2^{1} + O×2°

= 32 + 16 + 8 + 0 + 0 + 0 = (56)_{10 }d. (251)_{g} = 2 x 8^{2} + 5 x 8^{1} + 1 ×8°

= 128 + 40 + 1

= (169)_{10 }Descending order is (101)_{16} , (251)_{8}, (110)_{10}, (111ooo)_{2}

Question 15.

Find X, if(X)_{a} = (10111)_{2}+ (11011)_{2}– (111oo)_{2} (2)

Answer:

Question 16.

What are the methods of representing integers in computer memory? (2)

Answer:

There are three methods for representing an integer number in computer memory. They are:

- Sign and magnitude representation
- 1’s complement representation
- 2’s complement representation

Question 17.

Represent the following numbers in sign and magnitude method, l’s complement method and 2’s complement method. (3)

a. -19

b. +49

c. -97

d. -127

Answer:

**In sign and magnitude:**

- -19 = 110011
- +49 = 0110001
- -97 = 11100001
- -127 = 11111111

**In 1’s complement method: ** .

- -19 = 11101100
- +49 = 11001110
- -97 = 10011110
- -127 = 10000000

**In 2’s complement method:**

- -19 = 11101100 + 1 = 11101101
- +49 = 00110001
- -97 = 10011110 + 1 = 10011111
- -127 = 10000000 + 1 = 10000001

Question 18.

Find out the integer which is represented as (10011001)_{2} in sign and magnitude method. (1)

Answer:

-25

Question 19.

Explain the method of representing a floating point number in 32 bit computer. (2)

Answer:

A real number or floating point number can be represented in 32 bit word length computer. Here 24 bits are used for storing mantissa (among these the first bit is for sign) and 8 bits are used for storing exponent (first bit for sign).

Question 2o.

What are the methods of representing characters in computer memory? (3)

Answer:

Characters are representing as binary codes in computer memory. Various codes are ASCII (American Standard Code for Information Interchange), EBCDIC (Extended Binary Coded Decimal Interchange Code), ISCII (Indian Standard Code for Information Interchange/Indian Script Code for Information Interchange) and Unicode.

Question 21.

Briefly explain the significance of Unicode in character representation. (2)

Answer:

Unicode is used to represent all characters of written languages of the world and other symbols. Unicode originally used 16 bits. It is maintained by a non-profit organisation called the Unicode Consortium.

Question 22.

**Match the following:** (3)

Answer:

1 – b

2 – d

3 – a

4 – c

Question 23.

Find dual of following Boolean expressions: (3)

a. X . Y + Z

b. A.C + A.1 + A.C

c. (A+0).(A.1. )

Answer:

a. X + Y . Z

b. A + A+o.A + C

c. (A . 1) + (A + 0 + )

Question 24.

Find complement of following Boolean expressions. (2)

a. .

b.

Answer:

Question 25.

Construct logic circuit for the following Boolean expression. (3)

i.

ii.

Answer:

Question 26.

Why are NAND and NOR gates called universal gates? Justify with an example. (2)

Answer:

The NAND and NOR gates are called universal gates. A universal gate is a gate which can implement any Boolean function without using any other gate type. eg., AND gate can be implemented using NAND gate.

Question 27.

Briefly explain different methods for representing numbers in computer memory. (5)

Answer:

Numbers can be represented in memory in two ways.

**1. Representation of integers:** There are three methods for representing an integer number in computer memory. They are:

- Sign and magnitude representation:

In this method, first bit from left (MSB) is used for representing sign of integer and remaining 7-bits are used for representing magnitude of integer. For negative integers sign bit is 1 and for positive integers sign bit is 0. - 1’s complement representation: In this method, first find binary equivalent of absolute value of integer. If number of digits in binary equivalent is less than 8, provide zero(s) at the left to make it 8-bit form, l’s complement of a binary number is obtained by replacing every 0 with 1 and every 1 with o.
- 2’s complement representation: In this method, first find binary equivalent of absolute value of integer and write it in 8-bit form. If the number is negative, it is represented as 2’s complement of 8-bit form binary. If the number is positive, 8-bit form binary itself is the representation. 2’s complement of a binary number is calculated by adding 1 to its l’s complement.

**2. Representation floating point numbers:**

A floating point number or real number consists of an integer part and a fractional part. A real number can be written in a special notation called the floating point notation. Any number in this notation contains two parts, mantissa and exponent.

Question 28.

Briefly explain different methods for representing characters in computer memory. (5)

Answer:

**Characters can be represented as:**

1. ASCII (American Standard Code for Information Interchange) uses 7 bits to represent each character in computer memory. A unique integer number is assigned to each character. This number called ASCII code of that character is converted into binary for storing in memory. New version ASCII-8, also called extended ASCII, which uses 8 bits for each character, eg., ASCII code for A is 65.

2. EBCDIC (Extended Binary Coded Decimal Interchange Code) is similar to ASCII and is an 8 bit code used in computers. If ASCII coded data is to be used in a computer which uses EBCDIC representation, it is necessary to trans¬form ASCII code to EBCDIC code and vice versa.

3. ISCII (Indian Standard Code for Information Interchange/Indian Script Code for Information Interchange) is an encoding scheme for representing various writing systems of India. ISCII uses 8-bits for data representation. Nowadays ISCII has been replaced by Unicode.

4. Unicode is used to represent all characters of written languages of the world and other symbols. Unicode originally used 16 bits. It is maintained by a non-profit organisation called the Unicode Consortium.

Question 29.

What are the file formats for storing image, sound and video data? (3)

Answer:

**Representation of audio, image, video:**

- Image file consists of two parts header information and image data, eg., JPEG (Joint Picture Experts Group), bitmap file format (BMP), Tagged Image File Format (TIFF), Graphics Interchange Format (GIF), Portable (Public) Network Graphic (PNG).
- Audio file describes a format, referred to as the ‘container format’, for storing digital audio data, eg., Digital audio data can be stored in different file formats like WAV, MP3, MIDI (Musical Instrument Digital Interface), AIFF, etc.
- Video can be represented in AVI (Audio Video Interleave).

Question 30.

Find out the logical statements(s) from the following. (3)

a. Why are you late?

b. Will you come with me to market?

c. India is my country.

d. Go to class room.

Answer:

a. Boolean variables

b. Logical Constance

c. Logical Constance

d. Logical Constance

Question 31.

Prove that NOR gate is a universal gate by implementing all the basic gates. (3)

Answer:

NOR gate is a universal gate. Because all the basic gates can be implemented using NOR gate.

Question 32.

Give logic symbol, Boolean expression and truth table for three input AND gate. (5)

Answer:

Boolean expression is,Y=A.B.C

Logic Symbol:

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