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Chapter 2

Number System - An Introduction

Class 7 - APC Understanding Computer Studies


Tick (✓) the correct answer

Question 1

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

  1. 2
  2. 10 ✓
  3. 16
  4. All of the above

Question 2

The base of an octal number is represented by:

  1. 2
  2. 8 ✓
  3. 7
  4. None

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 the above

Question 4

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

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

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 the above

Question 6

The base of a hexa-decimal number is represented by

  1. H16
  2. 16 ✓
  3. 15
  4. None

Question 7

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

  1. 11 ✓
  2. 12
  3. 14
  4. 13

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

Question 9

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

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

Question 10

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

  1. 14
  2. 15
  3. 11 ✓
  4. 12

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 a 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

Octal
Digit
Binary
Equivalent
5
7
1
6
3
Hexadecimal
Digit
Binary
Equivalent
8
11
4
15
9

Answer

Octal
Digit
Binary
Equivalent
5101
7111
1001
6110
3011
Hexadecimal
Digit
Binary
Equivalent
81000
111011
40100
151111
91001

Convert the following to their binary equivalents

Question 1

(78)10

Answer

2QuotientRemainder
2780 (LSB)
2391
2191
291
240
220
211 (MSB)
 0 

Therefore, (78)10 = (1001110)2

Question 2

(99)10

Answer

2QuotientRemainder
2991 (LSB)
2491
2240
2120
260
231
211 (MSB)
 0 

Therefore, (99)10 = (1100011)2

Question 3

(141)10

Answer

2QuotientRemainder
21411 (LSB)
2700
2351
2171
280
240
220
211 (MSB)
 0 

Therefore, (141)10 = (10001101)2

Question 4

(123)10

Answer

2QuotientRemainder
21231 (LSB)
2611
2300
2151
271
231
211 (MSB)
 0 

Therefore, (123)10 = (1111011)2

Convert the following to their decimal equivalents

Question 1

(10101)2 to ( )10

Answer

Binary
No
PowerValueResult
1 (LSB)2011x1=1
02120x2=0
12241x4=4
02380x8=0
1 (MSB)24161x16=16

Equivalent decimal number = 1 + 4 + 16 = 21

Therefore, (10101)2 = (21)10

Question 2

(10000)2 to ( )10

Answer

Binary
No
PowerValueResult
0 (LSB)2010x1=0
02120x2=0
02241x4=4
02380x8=0
1 (MSB)24161x16=16

Equivalent decimal number = 16

Therefore, (10000)2 = (16)10

Question 3

(11001)2 to ( )10

Answer

Binary
No
PowerValueResult
1 (LSB)2011x1=1
02120x2=0
02240x4=0
12381x8=8
1 (MSB)24161x16=16

Equivalent decimal number = 1 + 8 + 16 = 25

Therefore, (11001)2 = (25)10

Question 4

(101010)2 to ( )10

Answer

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

Therefore, (101010)2 = (42)10

Convert the following to Decimal numbers

Question 1

(510)8

Answer

Octal
No
PowerValueResult
0 (LSB)8010x1=0
18181x8=8
5 (MSB)82645x64=320

Equivalent decimal number = 8 + 320 = 328

Therefore, (510)8 = (328)10

Question 2

(ABC)16

Answer

Hexadecimal
Number
PowerValueResult
C (12)160112x1=12
B (11)1611611x16=176
A (10)16225610x256=2560

Equivalent decimal number = 12 + 176 + 2560 = 2748

Therefore, (ABC)16 = (2748)10

Question 3

(1001011)2

Answer

Binary
No
PowerValueResult
1 (LSB)2011x1=1
12121x2=2
02240x4=0
12381x8=8
024160x16=0
025320x32=0
1 (MSB)26641x64=64

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

Therefore, (1001011)2 = (75)10

Question 4

(CD7)16

Answer

Hexadecimal
Number
PowerValueResult
716017x1=7
D (13)1611613x16=208
C (12)16225612x256=3072

Equivalent decimal number = 7 + 208 + 3072 = 3287

Therefore, (CD7)16 = (3287)10

Question 5

(101001)2 to ( )10

Answer

Binary
No
PowerValueResult
1 (LSB)2011x1=1
02120x2=0
02240x4=0
12381x8=8
024160x16=0
1 (MSB)25321x32=32

Equivalent decimal number = 1 + 8 + 32 = 41

Therefore, (101001)2 = (41)10

Question 6

(1100111)2 to ( )10

Answer

Binary
No
PowerValueResult
1 (LSB)2011x1=1
12121x2=2
12241x4=4
02380x8=0
024160x16=0
125321x32=32
1 (MSB)26641x64=64

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

Therefore, (1100111)2 = (103)10

Perform the following

Question 1

(342)8 to ( )2

Answer

Octal
Number
Binary
Equivalent
2010
4100
3011

Therefore, (342)8 = (011undefined100undefined010undefined\bold{\underlinesegment{011}}\medspace\bold{\underlinesegment{100}}\medspace\bold{\underlinesegment{010}})2

Question 2

(203)8 to ( )2

Answer

Octal
Number
Binary
Equivalent
3011
0000
2010

Therefore, (203)8 = (010undefined000undefined011undefined\bold{\underlinesegment{010}}\medspace\bold{\underlinesegment{000}}\medspace\bold{\underlinesegment{011}})2

Question 3

(9AD)16 to ( )2

Answer

Hexadecimal
Number
Binary
Equivalent
D (13)1101
A (10)1010
91001

Therefore, (9AD)16 = (1001undefined1010undefined1101undefined\bold{\underlinesegment{1001}}\medspace\bold{\underlinesegment{1010}}\medspace\bold{\underlinesegment{1101}})2

Question 4

(157)8 to ( )2

Answer

Octal
Number
Binary
Equivalent
7111
5101
1001

Therefore, (157)8 = (001undefined101undefined111undefined\bold{\underlinesegment{001}}\medspace\bold{\underlinesegment{101}}\medspace\bold{\underlinesegment{111}})2

Question 5

(ABC)16 to ( )2

Answer

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

Therefore, (ABC)16 = (1010undefined1011undefined1100undefined\bold{\underlinesegment{1010}}\medspace\bold{\underlinesegment{1011}}\medspace\bold{\underlinesegment{1100}})2

Question 6

(DE)16 to ( )2

Answer

Hexadecimal
Number
Binary
Equivalent
E (14)1110
D (13)1101

Therefore, (DE)16 = (1101undefined1110undefined\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:

1100undefined1110undefined1111undefined\underlinesegment{1100} \quad \underlinesegment{1110} \quad \underlinesegment{1111}

Binary
Number
Equivalent
Hexadecimal
1111F (15)
1110E (14)
1100C (12)

Therefore, (110011101111)2 = (CEF)16

Question 2

(11010111100)2

Answer

Grouping in bits of 4:

0110undefined1011undefined1100undefined\underlinesegment{0110} \quad \underlinesegment{1011} \quad \underlinesegment{1100}

Binary
Number
Equivalent
Hexadecimal
1100C (12)
1011B (11)
01106

Therefore, (11010111100)2 = (6BC)16

Question 3

(89392)10

Answer

16QuotientRemainder
16893920
1655873
16349D (13)
16215
1611
 0 

Therefore, (89392)10 = (15D30)16

Question 4

(100101101110)2

Answer

Grouping in bits of 4:

1001undefined0110undefined1110undefined\underlinesegment{1001} \quad \underlinesegment{0110} \quad \underlinesegment{1110}

Binary
Number
Equivalent
Hexadecimal
1110E (14)
01106
10019

Therefore, (100101101110)2 = (96E)16

Question 5

(9894)10

Answer

16QuotientRemainder
1698946
16618A (10)
16386
1622
 0 

Therefore, (9894)10 = (26A6)16

Question 6

(4966)10

Answer

16QuotientRemainder
1649666
163106
16193
1611
 0 

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

Binary numberDecimal number
It uses 2 digits — 0 and 1.It uses 10 digits — 0 to 9.
It uses base 2.It uses base 10.

Question 3b

Give two differences between Octal number and Binary number

Answer

Octal numberBinary number
It uses 8 digits — 0 to 7.It uses 2 digits — 0 and 1.
It uses base 8.It uses base 2.
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