NCERT Textbook: Encoding Schemes and Number System | Computer Science for Class 11 - Humanities/Arts PDF Download

 Page 1


2.1 Introduct Ion Have you ever thought how the keys on the computer 
keyboard that are in human recognisable form are 
interpreted by the computer system? This section briefly 
discusses text interpretation by the computer. 
We have learnt in the previous chapter that 
computer understands only binary language of 0s and 
1s. Therefore, when a key on the keyboard is pressed, it 
is internally mapped to a unique code, which is further 
converted to binary.
Example 2.1 When the key ‘A’ is pressed (Figure 2.1), it 
is internally mapped to a decimal value 65 (code value), 
which is then converted to its equivalent binary value 
for the computer to understand.
Figure 2.1: Encoding of data entered using keyboard
Similarly, when we press alphabet ‘?’ on hindi keyboard, 
internally it is mapped to a hexadecimal value 0905, 
whose binary equivalent is 0000100100000101.
So what is encoding? The mechanism of converting 
data into an equivalent cipher using specific code is 
“We owe a lot to the 
Indians, who taught us how 
to count, without which 
no worthwhile scientific 
discovery could have been 
made.”
–Albert Einstein
Chapter 2 
Encoding Schemes and 
Number System 
In this chapter
 » Introduction to 
Encoding
 » UNICODE
 » Number System
 » Conversion 
Between Number 
Systems
Ch 2.indd   27 08-Apr-19   11:38:00 AM
2024-25
Page 2


2.1 Introduct Ion Have you ever thought how the keys on the computer 
keyboard that are in human recognisable form are 
interpreted by the computer system? This section briefly 
discusses text interpretation by the computer. 
We have learnt in the previous chapter that 
computer understands only binary language of 0s and 
1s. Therefore, when a key on the keyboard is pressed, it 
is internally mapped to a unique code, which is further 
converted to binary.
Example 2.1 When the key ‘A’ is pressed (Figure 2.1), it 
is internally mapped to a decimal value 65 (code value), 
which is then converted to its equivalent binary value 
for the computer to understand.
Figure 2.1: Encoding of data entered using keyboard
Similarly, when we press alphabet ‘?’ on hindi keyboard, 
internally it is mapped to a hexadecimal value 0905, 
whose binary equivalent is 0000100100000101.
So what is encoding? The mechanism of converting 
data into an equivalent cipher using specific code is 
“We owe a lot to the 
Indians, who taught us how 
to count, without which 
no worthwhile scientific 
discovery could have been 
made.”
–Albert Einstein
Chapter 2 
Encoding Schemes and 
Number System 
In this chapter
 » Introduction to 
Encoding
 » UNICODE
 » Number System
 » Conversion 
Between Number 
Systems
Ch 2.indd   27 08-Apr-19   11:38:00 AM
2024-25
Computer SCien Ce – Cla SS xi 28
called encoding. It is important to understand why 
code value 65 is used for the key “A” and not any other 
value? Is it same for all the keyboards irrespective of 
their make?
Yes, it is same for all the keyboards. This has been 
possible because of standard encoding schemes where 
each letter, numeral and symbol is encoded or assigned 
a unique code. Some of the well-known encoding 
schemes are described in the following sections.
2.1.1 American Standard Code for Information 
Interchange (ASCII)
In the early 1960s, computers had no way of 
communicating with each other due to different 
ways of representing keys of the keyboard. Hence, 
the need for a common standard was realised to 
overcome this shortcoming. Thus, encoding scheme 
ASCII was developed for standardising the character 
representation. ASCII is still the most commonly used 
coding scheme.
Initially ASCII used 7 bits to represent characters. 
Recall that there are only 2 binary digits (0 or 1). 
Therefore, total number of different characters on the 
English keyboard that can be encoded by 7-bit ASCII 
code is 2
7
 = 128. Table 2.1 shows some printable 
characters for ASCII code. But ASCII is able to encode 
character set of English language only.
Example 2.2 Encode the word DATA and convert 
the encoded value into binary values which can be 
understood by a computer. 
Table 2.1 ASCII code for some printable characters 
Character Decimal Value Character Decimal Value Character Decimal Value
Space 32 @ 64 ` 96
! 33 A 65 a 97
” 34 B 66 b 98
# 35 C 67 c 99
$ 36 D 68 d 100
% 37 E 69 e 101
& 38 F 70 f 102
‘ 39 G 71 g 103
( 40 H 72 h 104
) 41 I 73 i 105
Cipher means something 
converted to a coded form 
to hide/conceal it from 
others. It is also called 
encryption (converted to 
cipher) and sent to the 
receiver who in turn can 
decrypt it to get back the 
actual content. 
Ch 2.indd   28 08-Apr-19   11:38:00 AM
2024-25
Page 3


2.1 Introduct Ion Have you ever thought how the keys on the computer 
keyboard that are in human recognisable form are 
interpreted by the computer system? This section briefly 
discusses text interpretation by the computer. 
We have learnt in the previous chapter that 
computer understands only binary language of 0s and 
1s. Therefore, when a key on the keyboard is pressed, it 
is internally mapped to a unique code, which is further 
converted to binary.
Example 2.1 When the key ‘A’ is pressed (Figure 2.1), it 
is internally mapped to a decimal value 65 (code value), 
which is then converted to its equivalent binary value 
for the computer to understand.
Figure 2.1: Encoding of data entered using keyboard
Similarly, when we press alphabet ‘?’ on hindi keyboard, 
internally it is mapped to a hexadecimal value 0905, 
whose binary equivalent is 0000100100000101.
So what is encoding? The mechanism of converting 
data into an equivalent cipher using specific code is 
“We owe a lot to the 
Indians, who taught us how 
to count, without which 
no worthwhile scientific 
discovery could have been 
made.”
–Albert Einstein
Chapter 2 
Encoding Schemes and 
Number System 
In this chapter
 » Introduction to 
Encoding
 » UNICODE
 » Number System
 » Conversion 
Between Number 
Systems
Ch 2.indd   27 08-Apr-19   11:38:00 AM
2024-25
Computer SCien Ce – Cla SS xi 28
called encoding. It is important to understand why 
code value 65 is used for the key “A” and not any other 
value? Is it same for all the keyboards irrespective of 
their make?
Yes, it is same for all the keyboards. This has been 
possible because of standard encoding schemes where 
each letter, numeral and symbol is encoded or assigned 
a unique code. Some of the well-known encoding 
schemes are described in the following sections.
2.1.1 American Standard Code for Information 
Interchange (ASCII)
In the early 1960s, computers had no way of 
communicating with each other due to different 
ways of representing keys of the keyboard. Hence, 
the need for a common standard was realised to 
overcome this shortcoming. Thus, encoding scheme 
ASCII was developed for standardising the character 
representation. ASCII is still the most commonly used 
coding scheme.
Initially ASCII used 7 bits to represent characters. 
Recall that there are only 2 binary digits (0 or 1). 
Therefore, total number of different characters on the 
English keyboard that can be encoded by 7-bit ASCII 
code is 2
7
 = 128. Table 2.1 shows some printable 
characters for ASCII code. But ASCII is able to encode 
character set of English language only.
Example 2.2 Encode the word DATA and convert 
the encoded value into binary values which can be 
understood by a computer. 
Table 2.1 ASCII code for some printable characters 
Character Decimal Value Character Decimal Value Character Decimal Value
Space 32 @ 64 ` 96
! 33 A 65 a 97
” 34 B 66 b 98
# 35 C 67 c 99
$ 36 D 68 d 100
% 37 E 69 e 101
& 38 F 70 f 102
‘ 39 G 71 g 103
( 40 H 72 h 104
) 41 I 73 i 105
Cipher means something 
converted to a coded form 
to hide/conceal it from 
others. It is also called 
encryption (converted to 
cipher) and sent to the 
receiver who in turn can 
decrypt it to get back the 
actual content. 
Ch 2.indd   28 08-Apr-19   11:38:00 AM
2024-25
Encoding Sch Em ES and n umb Er Sy St Em 29
• ASCII value of D is 68 and its equivalent 7-bit 
binary code = 1000100
• ASCII value of A is 65 and its equivalent 7-bit binary 
code = 1000001
• ASCII value of T is 84 and its equivalent 7-bit binary 
code = 1010100
• ASCII value of A is 65 and its equivalent 7-bit binary 
code = 1000001
Replace each alphabet in DATA with its ASCII code value 
to get its equivalent ASCII code and with 7-bit binary 
code to get its equivalent binary number as shown in 
Table 2.2.
Activity 2.1
Explore and list down 
two font names for 
typing in any three 
Indian languages in 
UNICODE. 
Do we need to install 
some additional tool 
or font to type in an 
Indian language using 
UNICODE?
Think and Reflect
Why a character in 
UTF 32 takes more 
space than in UTF 16 
or UTF 8? 
Think and Reflect
Table 2.2 ASCII and Binary values for word DATA 
D A T A
ASCII Code 68 65 84 65
Binary Code 1000100 1000001 1010100 1000001
2.1.2 Indian Script Code for Information Interchange 
(ISCII)
In order to facilitate the use of Indian languages on 
computers, a common standard for coding Indian scripts 
called ISCII was developed in India during mid 1980s. 
It is an 8-bit code representation for Indian languages 
which means it can represent 2
8
=256 characters. It 
retains all 128 ASCII codes and uses rest of the codes 
(128) for additional Indian language character set. 
Additional codes have been assigned in the upper region 
(160– 255) for the ‘aksharas’ of the language. 
2.1.3 UNICODE
There were many encoding schemes, for character 
sets of different languages. But they were not able 
to communicate with each other, as each of them 
represented characters in their own ways. Hence, text 
created using one encoding scheme was not recognised 
by another machine using different encoding scheme.
Therefore, a standard called UNICODE has been 
developed to incorporate all the characters of every 
written language of the world. UNICODE provides a 
unique number for every character, irrespective of 
device (server, desktop, mobile), operating system 
(Linux, Windows, iOS) or software application (different 
Ch 2.indd   29 08-Apr-19   11:38:00 AM
2024-25
Page 4


2.1 Introduct Ion Have you ever thought how the keys on the computer 
keyboard that are in human recognisable form are 
interpreted by the computer system? This section briefly 
discusses text interpretation by the computer. 
We have learnt in the previous chapter that 
computer understands only binary language of 0s and 
1s. Therefore, when a key on the keyboard is pressed, it 
is internally mapped to a unique code, which is further 
converted to binary.
Example 2.1 When the key ‘A’ is pressed (Figure 2.1), it 
is internally mapped to a decimal value 65 (code value), 
which is then converted to its equivalent binary value 
for the computer to understand.
Figure 2.1: Encoding of data entered using keyboard
Similarly, when we press alphabet ‘?’ on hindi keyboard, 
internally it is mapped to a hexadecimal value 0905, 
whose binary equivalent is 0000100100000101.
So what is encoding? The mechanism of converting 
data into an equivalent cipher using specific code is 
“We owe a lot to the 
Indians, who taught us how 
to count, without which 
no worthwhile scientific 
discovery could have been 
made.”
–Albert Einstein
Chapter 2 
Encoding Schemes and 
Number System 
In this chapter
 » Introduction to 
Encoding
 » UNICODE
 » Number System
 » Conversion 
Between Number 
Systems
Ch 2.indd   27 08-Apr-19   11:38:00 AM
2024-25
Computer SCien Ce – Cla SS xi 28
called encoding. It is important to understand why 
code value 65 is used for the key “A” and not any other 
value? Is it same for all the keyboards irrespective of 
their make?
Yes, it is same for all the keyboards. This has been 
possible because of standard encoding schemes where 
each letter, numeral and symbol is encoded or assigned 
a unique code. Some of the well-known encoding 
schemes are described in the following sections.
2.1.1 American Standard Code for Information 
Interchange (ASCII)
In the early 1960s, computers had no way of 
communicating with each other due to different 
ways of representing keys of the keyboard. Hence, 
the need for a common standard was realised to 
overcome this shortcoming. Thus, encoding scheme 
ASCII was developed for standardising the character 
representation. ASCII is still the most commonly used 
coding scheme.
Initially ASCII used 7 bits to represent characters. 
Recall that there are only 2 binary digits (0 or 1). 
Therefore, total number of different characters on the 
English keyboard that can be encoded by 7-bit ASCII 
code is 2
7
 = 128. Table 2.1 shows some printable 
characters for ASCII code. But ASCII is able to encode 
character set of English language only.
Example 2.2 Encode the word DATA and convert 
the encoded value into binary values which can be 
understood by a computer. 
Table 2.1 ASCII code for some printable characters 
Character Decimal Value Character Decimal Value Character Decimal Value
Space 32 @ 64 ` 96
! 33 A 65 a 97
” 34 B 66 b 98
# 35 C 67 c 99
$ 36 D 68 d 100
% 37 E 69 e 101
& 38 F 70 f 102
‘ 39 G 71 g 103
( 40 H 72 h 104
) 41 I 73 i 105
Cipher means something 
converted to a coded form 
to hide/conceal it from 
others. It is also called 
encryption (converted to 
cipher) and sent to the 
receiver who in turn can 
decrypt it to get back the 
actual content. 
Ch 2.indd   28 08-Apr-19   11:38:00 AM
2024-25
Encoding Sch Em ES and n umb Er Sy St Em 29
• ASCII value of D is 68 and its equivalent 7-bit 
binary code = 1000100
• ASCII value of A is 65 and its equivalent 7-bit binary 
code = 1000001
• ASCII value of T is 84 and its equivalent 7-bit binary 
code = 1010100
• ASCII value of A is 65 and its equivalent 7-bit binary 
code = 1000001
Replace each alphabet in DATA with its ASCII code value 
to get its equivalent ASCII code and with 7-bit binary 
code to get its equivalent binary number as shown in 
Table 2.2.
Activity 2.1
Explore and list down 
two font names for 
typing in any three 
Indian languages in 
UNICODE. 
Do we need to install 
some additional tool 
or font to type in an 
Indian language using 
UNICODE?
Think and Reflect
Why a character in 
UTF 32 takes more 
space than in UTF 16 
or UTF 8? 
Think and Reflect
Table 2.2 ASCII and Binary values for word DATA 
D A T A
ASCII Code 68 65 84 65
Binary Code 1000100 1000001 1010100 1000001
2.1.2 Indian Script Code for Information Interchange 
(ISCII)
In order to facilitate the use of Indian languages on 
computers, a common standard for coding Indian scripts 
called ISCII was developed in India during mid 1980s. 
It is an 8-bit code representation for Indian languages 
which means it can represent 2
8
=256 characters. It 
retains all 128 ASCII codes and uses rest of the codes 
(128) for additional Indian language character set. 
Additional codes have been assigned in the upper region 
(160– 255) for the ‘aksharas’ of the language. 
2.1.3 UNICODE
There were many encoding schemes, for character 
sets of different languages. But they were not able 
to communicate with each other, as each of them 
represented characters in their own ways. Hence, text 
created using one encoding scheme was not recognised 
by another machine using different encoding scheme.
Therefore, a standard called UNICODE has been 
developed to incorporate all the characters of every 
written language of the world. UNICODE provides a 
unique number for every character, irrespective of 
device (server, desktop, mobile), operating system 
(Linux, Windows, iOS) or software application (different 
Ch 2.indd   29 08-Apr-19   11:38:00 AM
2024-25
Computer SCien Ce – Cla SS xi 30
browsers, text editors, etc.). Commonly used UNICODE 
encodings are UTF-8, UTF-16 and UTF-32. It is a superset 
of ASCII, and the values 0–128 have the same character 
as in ASCII. Unicode characters for Devanagari script 
is shown in Table 2.3. Each cell of the table contains a 
character along with its equivalent hexadecimal value.
Table 2.3 Unicode table for the Devanagari script
? 0900
? 0901
? 0902
?
0903
?
0904
?
0905
?
0906
?
0907
?
0908
?
0909
?
090A
?
090B
?
090C
?
090D
?
090E
?
090F
?
0910
?
0911
?
0912
?
0913
?
0914
?
0915
?
0916
?
0917
?
0918
?
0919
?
091A
?
091B
?
091C
?
091D
?
091E
?
091F
?
0920
?
0921
?
0922
?
0923
?
0924
?
0925
?
0926
?
0927
?
0928
?
0929
?
092A
?
092B
?
092C
?
092D
?
092E
?
092F
?
0930
?
0931
?
0932
?
0933
?
0934
?
0935
?
0936
?
0937
?
0938
?
0939
? 093A
?
093B
? 093C
?
093D
?
093E
?
093F
?
0940
? 0941
? 0942
? 0943
? 0944
? 0945
? 0946
? 0947
? 0948
?
0949
?
094A
?
094B
?
094C
? 094D
?
094E
?
094F
?
0950
? 0951
? 0952
? 0953
? 0954
? 0955
? 0956
? 0957
?
0958
?
0959
?
095A
?
095B
?
095C
?
095D
?
095E
?
095F
?
0960
?
0961
? 0962
? 0963
?
0964
?
0965
?
0966
?
0967
?
0968
?
0969
?
096A
?
096B
?
096C
?
096D
?
096E
?
096F
?
0970
?
0971
?
0972
?
0973
?
0974
?
0975
?
0976
?
0977
?
0978
?
0979
?
097A
?
097B
?
097C
?
097D
?
097E
?
097F
2.2 n umber Sy Stem Till now, we have learnt that each key (representing 
character, special symbol, function keys, etc.) of the 
keyboard is internally mapped to an ASCII code following 
an encoding scheme. This encoded value is further 
converted to its equivalent binary representation so 
that the computer can understand it. In Figure 2.1, the 
code for character “A” belongs to the decimal number 
system and its equivalent binary value belongs to the 
binary number system. A number system is a method 
to represent (write) numbers.
Every number system has a set of unique characters 
or literals. The count of these literals is called the radix 
or base of the number system. The four different number 
systems used in the context of computer are shown in 
Figure 2.2. These number systems are explained in 
subsequent sections.
Ch 2.indd   30 08-Apr-19   11:38:00 AM
2024-25
Page 5


2.1 Introduct Ion Have you ever thought how the keys on the computer 
keyboard that are in human recognisable form are 
interpreted by the computer system? This section briefly 
discusses text interpretation by the computer. 
We have learnt in the previous chapter that 
computer understands only binary language of 0s and 
1s. Therefore, when a key on the keyboard is pressed, it 
is internally mapped to a unique code, which is further 
converted to binary.
Example 2.1 When the key ‘A’ is pressed (Figure 2.1), it 
is internally mapped to a decimal value 65 (code value), 
which is then converted to its equivalent binary value 
for the computer to understand.
Figure 2.1: Encoding of data entered using keyboard
Similarly, when we press alphabet ‘?’ on hindi keyboard, 
internally it is mapped to a hexadecimal value 0905, 
whose binary equivalent is 0000100100000101.
So what is encoding? The mechanism of converting 
data into an equivalent cipher using specific code is 
“We owe a lot to the 
Indians, who taught us how 
to count, without which 
no worthwhile scientific 
discovery could have been 
made.”
–Albert Einstein
Chapter 2 
Encoding Schemes and 
Number System 
In this chapter
 » Introduction to 
Encoding
 » UNICODE
 » Number System
 » Conversion 
Between Number 
Systems
Ch 2.indd   27 08-Apr-19   11:38:00 AM
2024-25
Computer SCien Ce – Cla SS xi 28
called encoding. It is important to understand why 
code value 65 is used for the key “A” and not any other 
value? Is it same for all the keyboards irrespective of 
their make?
Yes, it is same for all the keyboards. This has been 
possible because of standard encoding schemes where 
each letter, numeral and symbol is encoded or assigned 
a unique code. Some of the well-known encoding 
schemes are described in the following sections.
2.1.1 American Standard Code for Information 
Interchange (ASCII)
In the early 1960s, computers had no way of 
communicating with each other due to different 
ways of representing keys of the keyboard. Hence, 
the need for a common standard was realised to 
overcome this shortcoming. Thus, encoding scheme 
ASCII was developed for standardising the character 
representation. ASCII is still the most commonly used 
coding scheme.
Initially ASCII used 7 bits to represent characters. 
Recall that there are only 2 binary digits (0 or 1). 
Therefore, total number of different characters on the 
English keyboard that can be encoded by 7-bit ASCII 
code is 2
7
 = 128. Table 2.1 shows some printable 
characters for ASCII code. But ASCII is able to encode 
character set of English language only.
Example 2.2 Encode the word DATA and convert 
the encoded value into binary values which can be 
understood by a computer. 
Table 2.1 ASCII code for some printable characters 
Character Decimal Value Character Decimal Value Character Decimal Value
Space 32 @ 64 ` 96
! 33 A 65 a 97
” 34 B 66 b 98
# 35 C 67 c 99
$ 36 D 68 d 100
% 37 E 69 e 101
& 38 F 70 f 102
‘ 39 G 71 g 103
( 40 H 72 h 104
) 41 I 73 i 105
Cipher means something 
converted to a coded form 
to hide/conceal it from 
others. It is also called 
encryption (converted to 
cipher) and sent to the 
receiver who in turn can 
decrypt it to get back the 
actual content. 
Ch 2.indd   28 08-Apr-19   11:38:00 AM
2024-25
Encoding Sch Em ES and n umb Er Sy St Em 29
• ASCII value of D is 68 and its equivalent 7-bit 
binary code = 1000100
• ASCII value of A is 65 and its equivalent 7-bit binary 
code = 1000001
• ASCII value of T is 84 and its equivalent 7-bit binary 
code = 1010100
• ASCII value of A is 65 and its equivalent 7-bit binary 
code = 1000001
Replace each alphabet in DATA with its ASCII code value 
to get its equivalent ASCII code and with 7-bit binary 
code to get its equivalent binary number as shown in 
Table 2.2.
Activity 2.1
Explore and list down 
two font names for 
typing in any three 
Indian languages in 
UNICODE. 
Do we need to install 
some additional tool 
or font to type in an 
Indian language using 
UNICODE?
Think and Reflect
Why a character in 
UTF 32 takes more 
space than in UTF 16 
or UTF 8? 
Think and Reflect
Table 2.2 ASCII and Binary values for word DATA 
D A T A
ASCII Code 68 65 84 65
Binary Code 1000100 1000001 1010100 1000001
2.1.2 Indian Script Code for Information Interchange 
(ISCII)
In order to facilitate the use of Indian languages on 
computers, a common standard for coding Indian scripts 
called ISCII was developed in India during mid 1980s. 
It is an 8-bit code representation for Indian languages 
which means it can represent 2
8
=256 characters. It 
retains all 128 ASCII codes and uses rest of the codes 
(128) for additional Indian language character set. 
Additional codes have been assigned in the upper region 
(160– 255) for the ‘aksharas’ of the language. 
2.1.3 UNICODE
There were many encoding schemes, for character 
sets of different languages. But they were not able 
to communicate with each other, as each of them 
represented characters in their own ways. Hence, text 
created using one encoding scheme was not recognised 
by another machine using different encoding scheme.
Therefore, a standard called UNICODE has been 
developed to incorporate all the characters of every 
written language of the world. UNICODE provides a 
unique number for every character, irrespective of 
device (server, desktop, mobile), operating system 
(Linux, Windows, iOS) or software application (different 
Ch 2.indd   29 08-Apr-19   11:38:00 AM
2024-25
Computer SCien Ce – Cla SS xi 30
browsers, text editors, etc.). Commonly used UNICODE 
encodings are UTF-8, UTF-16 and UTF-32. It is a superset 
of ASCII, and the values 0–128 have the same character 
as in ASCII. Unicode characters for Devanagari script 
is shown in Table 2.3. Each cell of the table contains a 
character along with its equivalent hexadecimal value.
Table 2.3 Unicode table for the Devanagari script
? 0900
? 0901
? 0902
?
0903
?
0904
?
0905
?
0906
?
0907
?
0908
?
0909
?
090A
?
090B
?
090C
?
090D
?
090E
?
090F
?
0910
?
0911
?
0912
?
0913
?
0914
?
0915
?
0916
?
0917
?
0918
?
0919
?
091A
?
091B
?
091C
?
091D
?
091E
?
091F
?
0920
?
0921
?
0922
?
0923
?
0924
?
0925
?
0926
?
0927
?
0928
?
0929
?
092A
?
092B
?
092C
?
092D
?
092E
?
092F
?
0930
?
0931
?
0932
?
0933
?
0934
?
0935
?
0936
?
0937
?
0938
?
0939
? 093A
?
093B
? 093C
?
093D
?
093E
?
093F
?
0940
? 0941
? 0942
? 0943
? 0944
? 0945
? 0946
? 0947
? 0948
?
0949
?
094A
?
094B
?
094C
? 094D
?
094E
?
094F
?
0950
? 0951
? 0952
? 0953
? 0954
? 0955
? 0956
? 0957
?
0958
?
0959
?
095A
?
095B
?
095C
?
095D
?
095E
?
095F
?
0960
?
0961
? 0962
? 0963
?
0964
?
0965
?
0966
?
0967
?
0968
?
0969
?
096A
?
096B
?
096C
?
096D
?
096E
?
096F
?
0970
?
0971
?
0972
?
0973
?
0974
?
0975
?
0976
?
0977
?
0978
?
0979
?
097A
?
097B
?
097C
?
097D
?
097E
?
097F
2.2 n umber Sy Stem Till now, we have learnt that each key (representing 
character, special symbol, function keys, etc.) of the 
keyboard is internally mapped to an ASCII code following 
an encoding scheme. This encoded value is further 
converted to its equivalent binary representation so 
that the computer can understand it. In Figure 2.1, the 
code for character “A” belongs to the decimal number 
system and its equivalent binary value belongs to the 
binary number system. A number system is a method 
to represent (write) numbers.
Every number system has a set of unique characters 
or literals. The count of these literals is called the radix 
or base of the number system. The four different number 
systems used in the context of computer are shown in 
Figure 2.2. These number systems are explained in 
subsequent sections.
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Encoding Sch Em ES and n umb Er Sy St Em 31
Number systems are also called positional number 
system because the value of each symbol (i.e., digit and 
alphabet) in a number depends upon its position within 
the number. Number may also have a fractional part 
similar to decimal numbers used by us. The symbol at 
the right most position in the integer part in a given 
number has position 0. The value of position (also called 
position value) in the integer part increases from right 
to left by 1. On the other hand, the first symbol in the 
fraction part of the number has position number –1, 
which decreases by 1 while reading fraction part from 
left to right. Each symbol in a number has a positional 
value, which is computed using its position value and 
the base value of the number system. The symbol at 
position number 3 in a decimal system with base 10 has 
positional value 10
3
. Adding the product of positional 
value and the symbol 
value results in 
the given number. 
Figure 2.3 shows 
the computation 
of decimal number 
123.45 using its 
positional value.
2.2.1 Decimal Number System
The decimal number system is used in our day-to-day 
life. It is known as base-10 system since 10 digits (0 to 
9) are used. A number is presented by its two values 
— symbol value (any digit from 0 to 9) and positional 
value (in terms of base value). Figure 2.4 shows the 
integer and fractional part of decimal number 237.25 
alongwith computation of the decimal number using 
positional values.
Digit 1 2 3 . 4 5
Position Number 2 1 0 –1 –2
Positional Value (10)
2
(10)
1
(10)
0
(10)
-1
(10)
-2
Add the product of positional value and corresponding digit to get 
decimal number.
                1 × 10
2
 + 2 × 10
1
 + 3 × 10
0
 + 4 × 10
-1
 + 5 × 10
-2
 = (123.45)
10
Figure 2.3: Computation of decimal number using its positional value
Figure 2.2: Four different number systems 
0–9 and A–F
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