Choose the correct option

Question 1

In a decimal number system, the base of a number is represented by

1. 2
2. 10
3. 16
4. All of them

Answer

10

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

Question 2

The base of an octal number is represented by:

1. 2
2. 8
3. 7
4. None

Answer

8

Reason — The octal number system uses 8 digits (from 0 to 7) hence its has a base of 8.

Question 3

To convert an octal number to its binary equivalent, each octal digit is expressed as

1. 3 bits form
2. 4 bits form
3. 8 bits form
4. All of them

Answer

3 bits form

Reason — Since the digits from 0 to 7 need a maximum of 3 bits to be represented in binary form hence in Octal to Binary conversion each octal digit is expressed as 3 bits form.

Question 4

Sixteen raised to the power zero (16⁰) is equivalent to

1. 0
2. 1
3. 0 and 1
4. None

Answer

1

Reason — Any number raised to the power of 0 is 1.

Question 5

An octal number system uses the digits from

1. 0 to 8
2. 1 to 8
3. 0 to 7
4. All of them

Answer

0 to 7

Reason — The octal number system is a base 8 number system as it uses the digits from 0 to 7.

Question 6

The base of a hexa-decimal number is represented by

1. H16
2. 16
3. 15
4. None

Answer

16

Reason — The hexa-decimal number system uses 16 digits (from 0 to 15) hence its has a base of 16.

Question 7

In a hexa-decimal number system, 'B' represents the digit

1. 11
2. 12
3. 14
4. 13

Answer

11

Reason — In hexa-decimal number system, the digits 0 to 15 are represented by the letters A to F.

Question 8

To express a hexa-decimal number to its binary equivalent, each hexa-decimal digit is expressed as

1. 2 bits form
2. 3 bits form
3. 4 bits form
4. None

Answer

4 bits form

Reason — Since the digits from 0 to 15 need a maximum of 4 bits to be represented in binary form hence in Hexa-decimal to Binary conversion each hexa-decimal digit is expressed as 4 bits form.

Question 9

The binary equivalent of a hexa-decimal digit 12(C) is represented by

1. 1010
2. 1011
3. 1101
4. 1100

Answer

1100

Reason — The hexa-decimal digit 12(C) is represented as 1100.

Question 10

The hexa-decimal equivalent digit of 1011 (4 bits form) is

1. 14
2. 15
3. 11
4. 12

Answer

11

Reason — The hexa-decimal equivalent digit of 1011 (4 bits form) is 11.

Fill in the blanks

Question 1

The binary system consists of two digits 0 and 1.

Question 2

A decimal number system uses the digits from 0 to 9.

Question 3

The base in the decimal number system is written as 10.

Question 4

A binary number system is written with 2 as the base.

Question 5

In a decimal to binary conversion, the first remainder is known as Least Significant Bit (LSB) and the last remainder is Most Significant Bit (MSB).

Question 6

2⁰ = 1

Complete the following tables

Answer

Case-Study Based Questions

Question 1

Your teacher has assigned you a task to give a presentation on conversion of octal numbers into binary numbers and vice-versa. You are asked to create some aids to support your presentation. You have created two tables, Table 1 and Table 2, to demonstrate some examples.

In the above tables, some entries have either been missed or incorrect. Answer the following questions based on the above case:

(a) What will be filled in the blank space of Table 1?

(b) Find and rectify the incorrect binary equivalent in Table 1.

(c) Fill the appropriate octal equivalent in the blank space of Table 2.

(d) Find and rectify the incorrect octal equivalent in Table 2.

Answer

(a) 101

(b) In Table 1, the binary equivalent of octal number 3 is incorrect. The correct value is 011.

(c) 4

(d) In Table 2, the octal equivalent of binary number 011 is incorrect. The correct value is 3.

Convert the following to their binary equivalents

Question 1

(78)₁₀

Answer

Therefore, (78)₁₀ = (1001110)₂

Question 2

(99)₁₀

Answer

Therefore, (99)₁₀ = (1100011)₂

Question 3

(141)₁₀

Answer

Therefore, (141)₁₀ = (10001101)₂

Question 4

(123)₁₀

Answer

Therefore, (123)₁₀ = (1111011)₂

Convert the following to their decimal equivalents

Question 1

(10101)₂

Answer

Equivalent decimal number = 1 + 4 + 16 = 21

Therefore, (10101)₂ = (21)₁₀

Question 2

(10000)₂

Answer

Equivalent decimal number = 16

Therefore, (10000)₂ = (16)₁₀

Question 3

(11001)₂

Answer

Equivalent decimal number = 1 + 8 + 16 = 25

Therefore, (11001)₂ = (25)₁₀

Question 4

(101010)₂

Answer

Equivalent decimal number = 2 + 8 + 32 = 42

Therefore, (101010)₂ = (42)₁₀

Convert the following to Decimal numbers

Question 1

(510)₈

Answer

Equivalent decimal number = 8 + 320 = 328

Therefore, (510)₈ = (328)₁₀

Question 2

(ABC)₁₆

Answer

Equivalent decimal number = 12 + 176 + 2560 = 2748

Therefore, (ABC)₁₆ = (2748)₁₀

Question 3

(1001011)₂

Answer

Equivalent decimal number = 1 + 2 + 8 + 64 = 75

Therefore, (1001011)₂ = (75)₁₀

Question 4

(CD7)₁₆

Answer

Equivalent decimal number = 7 + 208 + 3072 = 3287

Therefore, (CD7)₁₆ = (3287)₁₀

Question 5

(101001)₂

Answer

Equivalent decimal number = 1 + 8 + 32 = 41

Therefore, (101001)₂ = (41)₁₀

Question 6

(1100111)₂

Answer

Equivalent decimal number = 1 + 2 + 4 + 32 + 64 = 103

Therefore, (1100111)₂ = (103)₁₀

Convert the following to binary numbers

Question 1

(342)₈

Answer

Therefore, (342)₈ = ($\bold{\underlinesegment{011}}\medspace\bold{\underlinesegment{100}}\medspace\bold{\underlinesegment{010}}$)₂

Question 2

(203)₈

Answer

Therefore, (203)₈ = ($\bold{\underlinesegment{010}}\medspace\bold{\underlinesegment{000}}\medspace\bold{\underlinesegment{011}}$)₂

Question 3

(9AD)₁₆

Answer

Therefore, (9AD)₁₆ = ($\bold{\underlinesegment{1001}}\medspace\bold{\underlinesegment{1010}}\medspace\bold{\underlinesegment{1101}}$)₂

Question 4

(157)₈

Answer

Therefore, (157)₈ = ($\bold{\underlinesegment{001}}\medspace\bold{\underlinesegment{101}}\medspace\bold{\underlinesegment{111}}$)₂

Question 5

(ABC)₁₆

Answer

Therefore, (ABC)₁₆ = ($\bold{\underlinesegment{1010}}\medspace\bold{\underlinesegment{1011}}\medspace\bold{\underlinesegment{1100}}$)₂

Question 6

(DE)₁₆

Answer

Therefore, (DE)₁₆ = ($\bold{\underlinesegment{1101}}\medspace\bold{\underlinesegment{1110}}$)₂

Convert the following to their hexa-decimal equivalent

Question 1

(110011101111)₂

Answer

Grouping in bits of 4:

$\underlinesegment{1100} \quad \underlinesegment{1110} \quad \underlinesegment{1111}$

Therefore, (110011101111)₂ = (CEF)₁₆

Question 2

(11010111100)₂

Answer

Grouping in bits of 4:

$\underlinesegment{0110} \quad \underlinesegment{1011} \quad \underlinesegment{1100}$

Therefore, (11010111100)₂ = (6BC)₁₆

Question 3

(89392)₁₀

Answer

Therefore, (89392)₁₀ = (15D30)₁₆

Question 4

(100101101110)₂

Answer

Grouping in bits of 4:

$\underlinesegment{1001} \quad \underlinesegment{0110} \quad \underlinesegment{1110}$

Therefore, (100101101110)₂ = (96E)₁₆

Question 5

(9894)₁₀

Answer

Therefore, (9894)₁₀ = (26A6)₁₆

Question 6

(4966)₁₀

Answer

Therefore, (4966)₁₀ = (1366)₁₆

Short Answer Questions

Question 1

What are the different types of number systems that a computer deals with?

Answer

The different types of number systems are:

1. Binary Number System
2. Octal Number System
3. Decimal Number System
4. Hexadecimal Number System

Question 2

What is meant by the following terms? Give an example of each.

(a) An octal number
(b) A hexa-decimal number

Answer

(a) An Octal number — An octal number uses 8 types of digits — 0, 1, 2, 3, 4, 5, 6, 7. It is represented with base 8.

(b) A hexa-decimal number — A Hexa-decimal number uses 16 types of digits (0 to 15). To represent digits from 10 to 15 it uses letters from A to F respectively. It is represented with base 16.

Question 3a

Give two differences between Binary number and Decimal number

Answer

Question 3b

Give two differences between Octal number and Binary number

Answer