Data Representation and Boolean Logic

Solutions for Computer Science, Class 11, CBSE

Assertions And Reasons

6 questions

Question 1

Assertion (A): Data is stored inside a computer in the form of 0s and 1s.

Reasoning (R): Number system is a technique of representing numbers in different forms.

  1. Both A and R are true and R is the correct explanation of A.
  2. Both A and R are true but R is not the correct explanation of A.
  3. A is true but R is false.
  4. A is false but R is true.
Assertions And Reasons

Answer:

Both A and R are true but R is not the correct explanation of A.

Explanation
Data inside a computer gets stored and manipulated in digital (binary) form (0s and 1s). Number systems are the techniques to represent numbers in the computer system architecture. Every number system includes a set of unique characters or literals. It is a way to represent a number in different forms.

Question 2

Assertion (A): The base/radix of binary number system is 2.

Reasoning (R): Binary number system has only two digits, i.e., 1 and 0.

  1. Both A and R are true and R is the correct explanation of A.
  2. Both A and R are true but R is not the correct explanation of A.
  3. A is true but R is false.
  4. A is false but R is true.
Assertions And Reasons

Answer:

Both A and R are true and R is the correct explanation of A.

Explanation
The base of binary number system is 2 because it has only two digits, i.e., 1 and 0. Every number can be represented with 0 and 1 in binary number system.

Question 3

Assertion (A): The base/radix of Octal number system is 8 because it has 8 digits.

Reasoning (R): 342289 is an octal number.

  1. Both A and R are true and R is the correct explanation of A.
  2. Both A and R are true but R is not the correct explanation of A.
  3. A is true but R is false.
  4. A is false but R is true.
Assertions And Reasons

Answer:

A is true but R is false.

Explanation
The base of the octal number system is 8 because it has only 8 digits (0 to 7). The number 342289 is not an octal number because the octal number system only allows digits from 0 to 7, and 342289 contains digits outside this range (8 and 9).

Question 4

Assertion (A): If A+B=1 then its dual will be A.B=0.

Reasoning (R): In dual, 1 changes to 0 and 0 changes to 1. Similarly, (+) changes to (.) and (.) to (+).

  1. Both A and R are true and R is the correct explanation of A.
  2. Both A and R are true but R is not the correct explanation of A.
  3. A is true but R is false.
  4. A is false but R is true.
Assertions And Reasons

Answer:

Both A and R are true and R is the correct explanation of A.

Explanation
The dual of the Boolean expression A+B=1 is A⋅B=0. This is derived by applying the duality principle, which states that the dual of any boolean expression is obtained by interchanging the operations (+) and (.), and swapping the constants 1 and 0.

Question 5

Assertion (A): Unicode is used for multilingual encoding.

Reasoning (R): Unicode provides a unique number for all the characters of every written language of the world.

  1. Both A and R are true and R is the correct explanation of A.
  2. Both A and R are true but R is not the correct explanation of A.
  3. A is true but R is false.
  4. A is false but R is true.
Assertions And Reasons

Answer:

Both A and R are true and R is the correct explanation of A.

Explanation
Unicode represents a single encoding scheme for all languages and characters. Unicode provides a unique number for every character irrespective of the platform, program and the language.

Question 6

Assertion (A): The number of symbols (digit and alphabet) used in a number system is called its radix/base.

Reasoning (R): Base value of a number system is used to distinguish a number in one number system from another number system.

  1. Both A and R are true and R is the correct explanation of A.
  2. Both A and R are true but R is not the correct explanation of A.
  3. A is true but R is false.
  4. A is false but R is true.
Assertions And Reasons

Answer:

Both A and R are true and R is the correct explanation of A.

Explanation
The number of symbols (digits and alphabets) used in a number system defines its radix or base. The base value of a number system helps in distinguishing numbers from different number systems, such as binary, octal, decimal, and hexadecimal.

Fill In The Blanks

10 questions

Question 1

In binary number system, the left-most bit is called the most significant bit.

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Answer:

Question 2

Base of a number is also known as radix of a number.

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Answer:

Question 3

The decimal system is composed of 10 symbols.

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Answer:

Question 4

ASCII code is the most widely used alphanumeric code which is used in computers to translate text (letters, numbers and symbols).

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Answer:

Question 5

Unicode is a new universal coding standard adopted by all new Platforms.

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Answer:

Question 6

The AND operation is Boolean multiplication and the OR operation is Boolean addition.

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Answer:

Question 7

A statement is said to be a Boolean/Logical Statement if it has a definite value, which is either true or false.

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Answer:

Question 8

NOT gate has only one input and it complements an input signal.

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Answer:

Question 9

The values which are stored in binary variables are known as Boolean Constants.

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Answer:

Question 10

A Truth table is a representation of a Boolean function or expression containing all possible combinations of input values and their result in a tabular format.

Fill In The Blanks

Answer:

Multiple Choice Questions

13 questions

Question 1

What is information?

  1. Processed data
  2. Collection of programs
  3. Collection of instructions
  4. None of these
Multiple Choice Questions

Answer:

Processed data

Reason — Information is defined as processed data organized in a particular manner to generate meaningful piece of data.

Question 2

What is the base of binary number system?

  1. 8
  2. 10
  3. 2
  4. 16
Multiple Choice Questions

Answer:

2

Reason — The base of binary number system is 2 because it has only two digits.

Question 3

What is the base of decimal number system?

  1. 2
  2. 10
  3. 8
  4. 16
Multiple Choice Questions

Answer:

10

Reason — The decimal number system uses 10 digits (from 0 to 9) hence its has a base of 10.

Question 4

What is the base of octal number system?

  1. 2
  2. 10
  3. 8
  4. 16
Multiple Choice Questions

Answer:

8

Reason — The base of octal number system is 8 because it has only 8 digits.

Question 5

Which of the following is binary equivalent of (43)10?

  1. (101011)2
  2. (110011)2
  3. (110101)2
  4. (110010)2
Multiple Choice Questions

Answer:

(101011)2

Reason — To convert (43)10 from decimal to binary, we perform the following calculation:

243Remainder
2211 (LSB)
2101
250
221
210
 01 (MSB)

Therefore, (43)10 = (101011)2

Question 6

Which of the following is decimal equivalent of (10010)2?

  1. 28
  2. 18
  3. 20
  4. 22
Multiple Choice Questions

Answer:

18

Reason

Binary
No
PowerValueResult
0 (LSB)2010x1=0
12121x2=2
02240x4=0
02380x8=0
1 (MSB)24161x16=16

Equivalent decimal number = 2 + 16 = 18

Therefore, (10010)2 = (18)10.

Question 7

What is the full form of ISCII?

  1. International Standard Code for Information Interchange
  2. Indian Standard Code for Information Interchange
  3. International Script Code for Information Interchange
  4. None of these
Multiple Choice Questions

Answer:

Indian Standard Code for Information Interchange

Reason — The full form of ISCII is Indian Standard Code for Information Interchange.

Question 8

Hexadecimal number system is composed of?

  1. 2 symbols
  2. 10 symbols
  3. 8 symbols
  4. 16 symbols
Multiple Choice Questions

Answer:

16 symbols

Reason — A hexadecimal number system has sixteen (16) alphanumeric values from 0 to 9 and A to F.

Question 9

Which of the following is not a binary number?

  1. 1111
  2. 101
  3. 11E
  4. 000
Multiple Choice Questions

Answer:

11E

Reason — A binary number system only includes the digits 0 and 1. The number "11E" contains the letter 'E', which is not a valid digit in the binary system. Therefore, "11E" is not a binary number.

Question 10

Which numbering system uses numbers and letters as symbols?

  1. Decimal
  2. Binary
  3. Octal
  4. Hexadecimal
Multiple Choice Questions

Answer:

Hexadecimal

Reason — A hexadecimal number system has sixteen (16) alphanumeric values from 0 to 9 and A to F.

Question 11

Identify the logical/Boolean statement:

  1. 15+4=19
  2. I want to have coffee.
  3. Should I wear the mask or not?
  4. I love dogs.
Multiple Choice Questions

Answer:

Should I wear the mask or not?

Reason — A logical or Boolean statement is one that can be evaluated as either true or false. The statement "Should I wear the mask or not?" poses a question that requires a true or false answer, thus making it a logical or Boolean statement.

Question 12

The boolean expression of the following logic circuit is:

The boolean expression of the following logic circuit is: Data Representation and Boolean Logic, Computer Science with Python Preeti Arora Solutions CBSE Class 11.
  1. (A+B).C'+B
  2. A'B'+C+B'A
  3. A.B.C+(B'+C').A
  4. A+B+C'(A+B)
Multiple Choice Questions

Answer:

A.B.C+(B'+C').A

Reason — The above logic circuit is equivalent to the boolean expression A.B.C + (B'+C').A.

The boolean expression of the following logic circuit is: Data Representation and Boolean Logic, Computer Science with Python Preeti Arora Solutions CBSE Class 11.

Question 13

The following is a ............... Logical Gate.

The following is a Logical Gate. Data Representation and Boolean Logic, Computer Science with Python Preeti Arora Solutions CBSE Class 11.
  1. XOR
  2. NAND
  3. AND
  4. OR
Multiple Choice Questions

Answer:

AND

Reason — The above logic gate is an AND operator.

Solutions To Unsolved Questions

28 questions

Question 1

Convert decimal number into binary number.

(a) 52

(b) 44

(c) 25.80

(d) 62.325

Solutions To Unsolved Questions

Answer:

(a) 52

252Remainder
2260 (LSB)
2130
261
230
211
 01 (MSB)

Therefore, (52)10 = (110100)2.

(b) 44

244Remainder
2220 (LSB)
2110
251
221
210
 01 (MSB)

Therefore, (44)10 = (101100)2.

(c) 25.80

Let us first convert 25 into binary as shown below:

225Remainder
2121 (LSB)
260
230
211
 01 (MSB)

The binary equivalent of integer part (25)10 = (11001)2.

Now let us convert (0.80)10 into binary as shown below:

Multiply=IntegerFraction
0.80 x 2=10.6 (MSB)
0.6 x 2=10.2
0.2 x 2=00.4
0.4 x 2=00.8
0.8 x 2=10.6 (LSB)

The binary equivalent of fractional part (0.8)10 = (11001)2.

Therefore, (25.80)10 = (11001.11001)2.

(d) 62.325

Let us first convert 62 into binary as shown below:

262Remainder
2310 (LSB)
2151
271
231
211
 01 (MSB)

The binary equivalent of integer part (62)10 = (111110)2.

Now let us convert (0.325)10 into binary as shown below:

Multiply=IntegerFraction
0.325 x 2=00.65 (MSB)
0.65 x 2=10.3
0.3 x 2=00.6
0.6 x 2=10.2
0.2 x 2=00.4
0.4 x 2=00.8
0.8 x 2=10.6 (LSB)

The binary equivalent of fractional part (0.325)10 = (0101001)2.

Therefore, (62.325)10 = (111110.0101001)2.

Question 2

Convert decimal number into octal number.

(a) 911

(b) 540

(c) 61

(d) 132

Solutions To Unsolved Questions

Answer:

(a) 911

8911Remainder
81137 (LSB)
8141
816
 01 (MSB)

Therefore, (911)10 = (1617)8.

(b) 540

8540Remainder
8674 (LSB)
883
810
 01 (MSB)

Therefore, (540)10 = (1034)8.

(c) 61

861Remainder
875 (LSB)
 07 (MSB)

Therefore, (61)10 = (75)8.

(d) 132

8132Remainder
8164 (LSB)
820
 02 (MSB)

Therefore, (132)10 = (204)8.

Question 3

Convert decimal number into hexadecimal number.

(a) 132

(b) 3619

(c) 206

(d) 752

Solutions To Unsolved Questions

Answer:

(a) 132

16132Remainder
1684 (LSB)
 08 (MSB)

Therefore, (132)10 = (84)16.

(b) 3619

163619Remainder
162263 (LSB)
16142
 0E (14) (MSB)

Therefore, (3619)10 = (E23)16.

(c) 206

16206Remainder
1612E (14) (LSB)
 0C (12) (MSB)

Therefore, (206)10 = (CE)16.

(d) 752

16752Remainder
16470 (LSB)
162F (15)
 02 (MSB)

Therefore, (752)10 = (2F0)16

Question 4

Convert binary number into decimal number.

(a) 10111

(b) 111101

(c) 101010.011

(d) 101101

Solutions To Unsolved Questions

Answer:

(a) 10111

Binary
No
PowerValueResult
1 (LSB)2011x1=1
12121x2=2
12241x4=4
02380x8=0
1 (MSB)24161x16=16

Equivalent decimal number = 1 + 2 + 4 + 16 = 23

Therefore, (10111)2 = (23)10.

(b) 111101

Binary
No
PowerValueResult
1 (LSB)2011x1=1
02120x2=0
12241x4=4
12381x8=8
124161x16=16
1 (MSB)25321x32=32

Equivalent decimal number = 1 + 4 + 8 + 16 + 32 = 61

Therefore, (111101)2 = (61)10.

(c) 101010.011

For the integer part (101010):

Binary
No
PowerValueResult
0 (LSB)2010x1=0
12121x2=2
02240x4=0
12381x8=8
024160x16=0
1 (MSB)25321x32=32

Equivalent decimal number = 2 + 8 + 32 = 42

For the fractional part (0.011):

Binary
No
PowerValueResult
0 (LSB)2-10.50x0.5=0
12-20.251x0.25=0.25
12-30.1251x0.125=0.125

Equivalent decimal number = 0.25 + 0.125 = 0.375

Therefore, (101010.011)2 = (42.375)10.

(d) 101101

Binary
No
PowerValueResult
1 (LSB)2011x1=1
02120x2=0
12241x4=4
12381x8=8
024160x16=0
1 (MSB)25321x32=32

Equivalent decimal number = 1 + 4 + 8 + 32 = 45

Therefore, (101101)2 = (45)10.

Question 5

Convert octal number into decimal number.

(a) 75

(b) 321

(c) 142

(d) 205

Solutions To Unsolved Questions

Answer:

(a) 75

Octal
No
PowerValueResult
5 (LSB)8015x1=5
7 (MSB)8187x8=56

Equivalent decimal number = 5 + 56 = 61

Therefore, (75)8 = (61)10.

(b) 321

Octal
No
PowerValueResult
1 (LSB)8011x1=1
28182x8=16
3 (MSB)82643x64=192

Equivalent decimal number = 1 + 16 + 192 = 209

Therefore, (321)8 = (209)10.

(c) 142

Octal
No
PowerValueResult
2 (LSB)8012x1=2
48184x8=32
1 (MSB)82641x64=64

Equivalent decimal number = 2 + 32 + 64 = 98

Therefore, (142)8 = (98)10.

(d) 205

Octal
No
PowerValueResult
5 (LSB)8015x1=5
08180x8=56
2 (MSB)82642x64=128

Equivalent decimal number = 5 + 128 = 133

Therefore, (205)8 = (133)10.

Question 6

Convert hexadecimal number into decimal number.

(a) A2

(b) 13B

(c) 271

(d) 132

Solutions To Unsolved Questions

Answer:

(a) A2

Hexadecimal
Number
PowerValueResult
216012x1=2
A (10)1611610x16=160

Equivalent decimal number = 2 + 160 = 162

Therefore, (A2)16 = (162)10.

(b) 13B

Hexadecimal
Number
PowerValueResult
B (11)160111x1=11
3161163x16=48
11622561x256=256

Equivalent decimal number = 11 + 48 + 256 = 315

Therefore, (13B)16 = (315)10.

(c) 271

Hexadecimal
Number
PowerValueResult
116011x1=1
7161167x16=112
21622562x256=512

Equivalent decimal number = 1 + 112 + 512 = 625

Therefore, (271)16 = (625)10.

(d) 132

Hexadecimal
Number
PowerValueResult
216012x1=2
3161163x16=48
11622561x256=256

Equivalent decimal number = 2 + 48 + 256 = 306

Therefore, (132)16 = (306)10.

Question 7

Discuss UTF-8 encoding scheme. How is it different from UTF-32 encoding scheme?

Solutions To Unsolved Questions

Answer:

UTF-8 is a variable-width encoding that can represent every character in the Unicode character set. The code unit of UTF-8 is 8 bits (an octet). It uses 1 to 4 octets to represent code points, depending on their size. For example, it uses 1 byte for ASCII characters and up to 4 bytes for others. This makes UTF-8 a multi-byte encoding that efficiently handles different character sets.

UTF-32, in contrast, is a fixed-length encoding scheme that always uses exactly 4 bytes (32 bits) to represent all Unicode code points, regardless of their size, making it less space-efficient than UTF-8.

Question 8

What are Boolean constants?

Solutions To Unsolved Questions

Answer:

The values which are stored in binary variables are known as Boolean Constants. Therefore, the values true/false, yes/no or 1/0 are Boolean constants.

Question 9

What are Boolean operators? Explain AND, OR, NOT operators.

Solutions To Unsolved Questions

Answer:

Operators used in Boolean algebra are known as Boolean/Logical operators.

1. AND Operator — AND operator is a binary operator that operates on two variables and the operation performed by AND operator is known as logical multiplication. The symbol used for logical multiplication is dot(.) operator. The truth table for AND operator is as follows:

Truth Table

ABOutput A.B
000
010
100
111

The AND operation will result in true value (1) when both inputs are 1 (true/high) and for all other values it results in 0 (false/low).

2. OR Operator — The OR operator is a binary operator that operates on two variables and the operation performed by OR operator is known as logical addition. The symbol used for logical addition is plus (+) operator. The truth table for OR operator is as follows:

Truth Table

ABOutput A + B
000
011
101
111

The OR operation results in true value (1) when either of the inputs is 1 (true) or both the inputs are 1 (true/high), and for all other values of inputs it results in 0 (false/low).

3. NOT Operator — The NOT operator is a unary operator that operates on one variable and the operation performed by NOT operator is known as negation or complementation. The truth table for NOT operator is as follows:

Truth Table

AOutput A'
01
10

It means that the logical statements A and A' are opposite to each other. If the value of a variable A is 0, its complement would be 1, and if the value of the variable A is 1, its complement would be 0.

Question 10

What is the use of Hexadecimal number system in computers?

Solutions To Unsolved Questions

Answer:

The use of the hexadecimal number system in computers includes the following:

  1. The Hexadecimal number system is used in computers to specify memory addresses (which are 16-bit or 32-bit long). For example, a memory address 1101011010101111 is a big binary address but with hex it is D6AF which is easier to remember.
  2. The Hexadecimal number system is used to represent color codes. For example, FFFFFF represents White, FF0000 represents Red, etc.

Question 11

Verify the following using truth table:

(i) a.(a+b) = a

(ii) X.(Y+Z) = X.Y + X.Z

Solutions To Unsolved Questions

Answer:

(i) a.(a+b) = a

Truth Table

aba + ba.(a+b)a
00000
01100
10111
11111

As columns "a.(a+b)" and "a" have same values, hence the expression is proved.

(ii) X.(Y+Z) = X.Y + X.Z

Truth Table

XYZY+ZX.(Y+Z)X.YX.ZX.Y+X.Z
00000000
00110000
01010000
01110000
10000000
10111011
11011101
11111111

As columns X.(Y+Z) and X.Y+X.Z have same values, hence the expression is proved.

Question 12

Obtain the Boolean expression for the logic circuit shown below:

Obtain the Boolean expression for the logic circuit shown below: Data Representation and Boolean Logic, Computer Science with Python Preeti Arora Solutions CBSE Class 11.
Solutions To Unsolved Questions

Answer:

The boolean expression for the above logic circuit is xn.y+x.yn\overline{\overline{x^n.y} + \overline{x .y^n}}.

Obtain the Boolean expression for the logic circuit shown below: Data Representation and Boolean Logic, Computer Science with Python Preeti Arora Solutions CBSE Class 11.

Question 13

State De Morgan's law and prove it with a truth table.

Solutions To Unsolved Questions

Answer:

The first law states that when two (or more) input variables are OR'ed and negated, they are equivalent to the AND of the complements of the individual variables.

A+B\overline{A+B} = A.B\overline{A}.\overline{B}

Proof using truth table:

ABA'B'A + B(A+B)'A'.B'
0011011
0110100
1001100
1100100

The second law states that when two (or more) input variables are AND'ed and negated, they are equivalent to the OR of the complements of the individual variables.

A.B\overline{A.B} = A+B\overline{A} + \overline{B}

Proof using truth table:

ABA'B'A.B(A.B)'A' + B'
0011011
0110011
1001011
1100100

Question 14

What is the advantage of preparing a digital content in Indian language using UNICODE font?

Solutions To Unsolved Questions

Answer:

Following are the advantages of preparing a digital content in Indian language using UNICODE font:

  1. Unicode provides a universal character encoding standard, ensuring consistent display and compatibility across different platforms, devices, and applications.
  2. It supports a wide range of Indian scripts, allowing seamless text exchange and readability without font issues.
  3. Content prepared using Unicode can be easily indexed by search engines, improving accessibility and searchability.

Question 15

Encode the word 'COMPUTER' using ASCII and convert the encoded value into binary values.

Solutions To Unsolved Questions

Answer:

Representing the word 'COMPUTER' in ASCII values of its characters:

COMPUTER → 67 79 77 80 85 84 69 82

Binary Equivalent → 01000011 01001111 01001101 01010000 01010101 01010100 01000101 01010010

Explanation

ASCII value of C is 67 and its equivalent 7-bit binary code = 01000011
ASCII value of O is 79 and its equivalent 7-bit binary code = 01001111
ASCII value of M is 77 and its equivalent 7-bit binary code = 01001101
ASCII value of P is 80 and its equivalent 7-bit binary code = 01010000
ASCII value of U is 85 and its equivalent 7-bit binary code = 01010101
ASCII value of T is 84 and its equivalent 7-bit binary code = 01010100
ASCII value of E is 69 and its equivalent 7-bit binary code = 01000101
ASCII value of R is 82 and its equivalent 7-bit binary code = 01010010

Hence, binary value for the word 'COMPUTER' is 01000011 01001111 01001101 01010000 01010101 01010100 01000101 01010010.

Question 16

Give full form of ASCII and ISCII.

Solutions To Unsolved Questions

Answer:

ASCII — American Standard Code for Information Interchange

ISCII — Indian Standard Code for Information Interchange

Question 17

Draw a logic circuit of the following Boolean expression:

(i) (A.B\overline{B}) + (C + D\overline{D}) + (B.D\overline{D})

(ii) (A+B).(BC+D\overline{D})

Solutions To Unsolved Questions

Answer:

(i)

Draw a logic circuit of the following Boolean expression: Data Representation and Boolean Logic, Computer Science with Python Preeti Arora Solutions CBSE Class 11.

(ii)

Draw a logic circuit of the following Boolean expression: Data Representation and Boolean Logic, Computer Science with Python Preeti Arora Solutions CBSE Class 11.

Question 18

Write binary equivalent of the following octal numbers:

(a) 2306

(b) 5610

(c) 742

(d) 65.203

Solutions To Unsolved Questions

Answer:

(a) 2306

Octal
Number
Binary
Equivalent
6110
0000
3011
2010

Therefore, (2306)8 = (010undefined011undefined000undefined110undefined\bold{\underlinesegment{010}}\medspace\bold{\underlinesegment{011}}\medspace\bold{\underlinesegment{000}}\medspace\bold{\underlinesegment{110}})2.

(b) 5610

Octal
Number
Binary
Equivalent
0000
1001
6110
5101

Therefore, (5610)8 = (101undefined110undefined001undefined000undefined\bold{\underlinesegment{101}}\medspace\bold{\underlinesegment{110}}\medspace\bold{\underlinesegment{001}}\medspace\bold{\underlinesegment{000}})2.

(c) 742

Octal
Number
Binary
Equivalent
2010
4100
7111

Therefore, (742)8 = (111undefined100undefined010undefined\bold{\underlinesegment{111}}\medspace\bold{\underlinesegment{100}}\medspace\bold{\underlinesegment{010}})2.

(d) 65.203

Octal
Number
Binary
Equivalent
3011
0000
2010
5101
6110

Therefore, (65.203)8 = (110undefined101undefined.010undefined000undefined011undefined\bold{\underlinesegment{110}}\medspace\bold{\underlinesegment{101}}.\medspace\bold{\underlinesegment{010}}\medspace\bold{\underlinesegment{000}}\medspace\bold{\underlinesegment{011}})2.

Question 19

Write binary representation of the following hexadecimal numbers:

(a) 4026

(b) BCA1

(c) 98E

(d) 132.45

Solutions To Unsolved Questions

Answer:

(a) 4026

Hexadecimal
Number
Binary
Equivalent
60110
20010
00000
40100

Therefore, (4026)16 = (0100000000100110)2.

(b) BCA1

Hexadecimal
Number
Binary
Equivalent
10001
A (10)1010
C (12)1100
B (11)1011

B → 1011
C → 1100
A → 1010
1 → 0001

Therefore, (BCA1)16 = (1011110010100001)2.

(c) 98E

Hexadecimal
Number
Binary
Equivalent
E1110
81000
91001

Therefore, (98E)16 = (100110001110)2.

(d) 132.45

Hexadecimal
Number
Binary
Equivalent
50101
40100
20010
30011
10001

Therefore, (132.45)16 = (000100110010.01000101)2.

Question 20

Perform the following conversions from decimal number to other number systems:

(a) (54)10 = (?)2

(b) (120)10 = (?)2

(c) (76)10 = (?)8

(d) (889)10 = (?)8

(e) (789)10 = (?)16

(f) (108)10 = (?)16

Solutions To Unsolved Questions

Answer:

(a) (54)10

254Remainder
2270 (LSB)
2131
261
230
211
 01 (MSB)

Therefore, (54)10 = (110110)2.

(b) (120)10

2120Remainder
2600 (LSB)
2300
2150
271
231
211
 01 (MSB)

Therefore, (120)10 = (1111000)2.

(c) (76)10

876Remainder
894 (LSB)
811
 01 (MSB)

Therefore, (76)10 = (114)8.

(d) (889)10

8889Remainder
81111 (LSB)
8137
815
 01 (MSB)

Therefore, (889)10 = (1571)8.

(e) (789)10

16789Remainder
16495 (LSB)
1631
 03 (MSB)

Therefore, (789)10 = (315)16.

(f) (108)10

16108Remainder
16612 (C) (LSB)
 06 (MSB)

Therefore, (108)10 = (6C)16.

Question 21

Express the following binary numbers into their equivalent octal numbers:

(a) 100101111

(b) 111011010

(c) 1010011

(d) 10011101

Solutions To Unsolved Questions

Answer:

(a) 100101111

Grouping in bits of 3:

100undefined101undefined111undefined\underlinesegment{100} \quad \underlinesegment{101} \quad \underlinesegment{111}

Binary
Number
Equivalent
Octal
1004
1015
1117

Therefore, (100101111)2 = (457)8

(b) 111011010

Grouping in bits of 3:

111undefined011undefined010undefined\underlinesegment{111} \quad \underlinesegment{011} \quad \underlinesegment{010}

Binary
Number
Equivalent
Octal
1117
0113
0102

Therefore, (111011010)2 = (732)8

(c) 1010011

Grouping in bits of 3:

001undefined010undefined011undefined\underlinesegment{001} \quad \underlinesegment{010} \quad \underlinesegment{011}

Binary
Number
Equivalent
Octal
0011
0102
0113

Therefore, (1010011)2 = (123)8

(d) 10011101

Grouping in bits of 3:

010undefined011undefined101undefined\underlinesegment{010} \quad \underlinesegment{011} \quad \underlinesegment{101}

Binary
Number
Equivalent
Octal
0102
0113
1015

Therefore, (10011101)2 = (235)8

Question 22

Express the following binary numbers into their equivalent hexadecimal numbers:

(a) 1111101101100011

(b) 100000101011100

(c) 1000111010100011

(d) 111011111

Solutions To Unsolved Questions

Answer:

(a) 1111101101100011

Grouping in bits of 4:

1111undefined1011undefined0110undefined0011undefined\underlinesegment{1111} \quad \underlinesegment{1011} \quad \underlinesegment{0110} \quad \underlinesegment{0011}

Binary
Number
Equivalent
Hexadecimal
1111F
1011B
01106
00113

Therefore, (1111101101100011)2 = (FB63)16.

(b) 100000101011100

Grouping in bits of 4:

0100undefined0001undefined0101undefined1100undefined\underlinesegment{0100} \quad \underlinesegment{0001} \quad \underlinesegment{0101} \quad \underlinesegment{1100}

Binary
Number
Equivalent
Hexadecimal
01004
00011
01015
1100C

Therefore, (100000101011100)2 = (415C)16.

(c) 1000111010100011

Grouping in bits of 4:

1000undefined1110undefined1010undefined0011undefined\underlinesegment{1000} \quad \underlinesegment{1110} \quad \underlinesegment{1010} \quad \underlinesegment{0011}

Binary
Number
Equivalent
Hexadecimal
10008
1110E
1010A
00113

Therefore, (1000111010100011)2 = (8EA3)16.

(d) 111011111

Grouping in bits of 4:

0001undefined1101undefined1111undefined\underlinesegment{0001} \quad \underlinesegment{1101} \quad \underlinesegment{1111}

Binary
Number
Equivalent
Hexadecimal
00011
1101D
1111F

Therefore, (111011111)2 = (1DF)16.

Question 23

Express the following octal numbers into their equivalent decimal numbers.

(a) 145

(b) 6760

(c) 455

(d) 10.75

Solutions To Unsolved Questions

Answer:

(a) 145

Octal
No
PowerValueResult
5 (LSB)8015x1=5
48184x8=32
1 (MSB)82641x64=64

Equivalent decimal number = 5 + 32 + 64 = 101

Therefore, (145)8 = (101)10.

(b) 6760

Octal
No
PowerValueResult
0 (LSB)8010x1=0
68186x8=48
782647x64=448
6 (MSB)835126x512=3072

Equivalent decimal number = 48 + 448 + 3072 = 3568

Therefore, (6760)8 = (3568)10.

(c) 455

Octal
No
PowerValueResult
5 (LSB)8015x1=5
58185x8=40
4 (MSB)82644x64=256

Equivalent decimal number = 5 + 40 + 256 = 301

Therefore, (455)8 = (301)10.

(d) 10.75

Integer part:

Octal
No
PowerValueResult
0 (LSB)8010x1=0
1 (MSB)8181x8=8

Equivalent decimal number = 8

Fractional part:

Octal
No
PowerValueResult
7 (LSB)8-10.1257x0.125=0.875
5 (MSB)8-20.0156255x0.015625=0.078125

Equivalent decimal number = 0.875 + 0.078125 = 0.953125

Therefore, (10.75)8 = (8.953125)10.

Question 24

The Hexadecimal number system uses 16 literals (0 - 9, A - F). Write down its base value.

Solutions To Unsolved Questions

Answer:

The base value of the hexadecimal number system is 16.

Question 25

Explore and list the steps required to type in an Indian language using UNICODE.

Solutions To Unsolved Questions

Answer:

To insert any Indian language character using Unicode in Microsoft Word, the steps are:

  1. Click Insert → Symbol → More Symbol
  2. From the Symbols dialog that appears, select a Unicode supporting font and Indian language's subset.
  3. Choose desired character and click Insert.

Question 26

Convert the following base of number system:

(a) (1010100)10 = (...............)2

(b) (3674)8 = (...............)2

(c) (266)10 = (...............)8

(d) (9F2)16 = (...............)2

Solutions To Unsolved Questions

Answer:

(a) (1010100)10

21010100Remainder
25050500 (LSB)
22525250
21262621
2631310
2315651
2157821
278910
239451
219721
29860
24930
22461
21230
2611
2301
2150
271
231
211
 01 (MSB)

Therefore, (1010100)10 = (11110110100110110100)2.

​ (b) (3674)8

Octal
Number
Binary
Equivalent
4100
7111
6110
3011

Therefore, (3674)8 = (011undefined110undefined111undefined100undefined\bold{\underlinesegment{011}}\medspace\bold{\underlinesegment{110}}\medspace\bold{\underlinesegment{111}}\medspace\bold{\underlinesegment{100}})2.

(c) (266)10

8266Remainder
8332 (LSB)
841
 04 (MSB)

Therefore, (266)10 = (412)8.

(c) (9F2)16

Hexadecimal
Number
Binary
Equivalent
20010
F1111
91001

Therefore, (9F2)16 = (100111110010)2.

Question 27

Write the name of following law and verify using truth table:

a(b + c) = ab + ac

Solutions To Unsolved Questions

Answer:

a(b + c) = ab + ac is distributive law.

Truth Table

abcb+ca.(b+c)a.ba.ca.b + a.c
00000000
00110000
01010000
01110000
10000000
10111011
11011101
11111111

As columns "a(b + c)" and "ab + ac" have same values, hence the expression is proved.

Question 28

Draw the logic circuit for the following Boolean expression:

(X'+Y).Z + W'

Solutions To Unsolved Questions

Answer:

The logic circuit for the Boolean expression is shown below:

Draw the logic circuit for the following Boolean expression: Data Representation and Boolean Logic, Computer Science with Python Preeti Arora Solutions CBSE Class 11.

State True Or False

11 questions

Question 1

Binary data representation has only two symbols, 0 and 1.

State True Or False

Answer:

True

Reason — Binary data representation uses only two symbols, 0 and 1, because it is based on base 2. In base 2, each digit (bit) can only be one of two values: 0 or 1. These digits are combined to represent numbers and data, with each position representing a power of 2, similar to how base 10 uses powers of 10.

Question 2

ASCII, ISCII and UNICODE are the three internal storage representations.

State True Or False

Answer:

True

Reason — ASCII, ISCII, and UNICODE are three types of character encoding schemes used for internal storage representations.

Question 3

(128)8 is the representation of an octal number system.

State True Or False

Answer:

False

Reason — The digit '8' is not valid in the octal system because the octal number system only includes digits from 0 to 7. Therefore, (128)8 is not a valid octal number.

Question 4

The first 128 characters are the same in both the types of ASCII, i.e., ASCII-7 and ASCII-8.

State True Or False

Answer:

True

Reason — The first 128 characters (ranging from 0 to 127) in both ASCII-7 and ASCII-8 are identical. ASCII-7 uses 7 bits to represent characters, covering the first 128 characters. ASCII-8 uses 8 bits, allowing for 256 characters in total. However, the first 128 characters remain consistent between both versions.

Question 5

512 characters can be represented in ASCII-8.

State True Or False

Answer:

False

Reason — ASCII-8 uses 8 bits, allowing for a total of 256 characters to be represented.

Question 6

Unicode provides a consistent way of encoding multilingual plain text.

State True Or False

Answer:

True

Reason — Unicode provides a unique number for every character irrespective of the platform, program and the language.

Question 7

ABC is a valid Hexadecimal number.

State True Or False

Answer:

True

Reason — A hexadecimal number system has sixteen (16) alphanumeric values from 0-9 and A-F. Therefore, "ABC" is a valid hexadecimal number.

Question 8

A number with both integer and a fractional part has digits raised to both positive and negative powers of 2 in a decimal number system.

State True Or False

Answer:

False

Reason — In the decimal number system, a number with both integer and fractional parts has digits raised to positive powers of 10 for the integer part and negative powers of 10 for the fractional part.

Question 9

(52)16 is equivalent to 90 in decimal number system.

State True Or False

Answer:

False

Reason — To convert (52)16 from hexadecimal to decimal, we calculate:

5×161 + 2×160 = 5×16 + 2×1 = 80 + 2 = 82

Thus, (52)16 is equivalent to 82 in the decimal number system.

Question 10

A number system that uses eight digits-0, 1, 2, 3, 4, 5, 6, and 7—is called an octal number system.

State True Or False

Answer:

True

Reason — Octal number system has only eight digits from 0 to 7. Every number can be represented with 0, 1, 2, 3, 4, 5, 6, 7 in this number system.

Question 11

NAND and NOR are called universal gates.

State True Or False

Answer:

True

Reason — The NAND and NOR gates are called universal gates because any digital circuits can be implemented using these gates.