# Data Representation in Computers

This page contains the CBSE class 11 Computer Science with Python chapter 3, Data Representation in Computers . You can find the questions/answers/solutions for the chapter 3 of Unit 1 of CBSE class 11 Computer Science with Python in this page.
a)
What does ASCII stand for?
b)
What does the base of a Number system mean?
c)
What is the base of Decimal, Binary, Octal and Hexadecimal number systems?
d)
How many digits are there in a Binary number system?
e)
Which digits are used in Hexadecimal number system?
f)
What is Unicode? How is it useful?
g)
Distinguish between ASCII and ISCII.
h)
Do as directed :
Convert the Decimal number 781 to its Binary equivalent.
Convert Binary number 101101.001 to its decimal equivalent
Convert Octal number 321.7 into its Binary equivalent
Convert the Hexadecimal number 3BC into its Binary equivalent
Convert the Binary number 10011010.010101 to its Hexadecimal equivalent
Convert the Decimal number 345 into Octal number.
Convert the Decimal number 736 into Hexadecimal number.
Convert the Octal number 246.45 into Hexadecimal number.
Convert the Hexadecimal number ABF.C into Octal number.
Convert the Octal number 576 to Decimal.
Convert the Hexadecimal number A5C1 to Decimal.

Data Representation in Computers
a) What does ASCII stand for?
ASCII is an acronym for American Standard Code for Information Interchange. ASCII-7 uses a total of 7 bits of which 4 are zone bits and 3 are numeric bits and can represent 128 characters. ASCII-8 is an extension of ASCII-7 and can represent 256 characters.
b) What does the base of a Number system mean?
The base of a Number system, also called as radix, is the number of unique digits that are used to represent the numbers in a positional number system. The number of unique digits includes the digit zero (0) also. For instance, the binary system is represented by the digits 0 and 1 (Two numbers are used and hence the name binary). The octal system uses 0, 1, 2, 3, 4, 5, 6 and 7 (total of eight numbers and hence the name octal) to represent the numbers. The decimal system uses 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 (total of 10 digits and hence the name) to represent the numbers. The hexadecimal system uses 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E and F (total of 16 numbers and hence the name hexadecimal) to represent the numbers.

c) What is the base of Decimal, Binary, Octal and Hexadecimal number systems?
The following are the bases of the various number systems.
Number System
Decimal System
10
Binary System
2
Octal System
8
16
d) How many digits are there in a Binary number system?
There are two digits i.e. 0 and 1 in the binary number system.
e) Which digits are used in Hexadecimal number system?
The digits (to be specific it is a combination of digits and alphabets) used in the Hexadecimal number system are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E and F. In this A represents 10, B represents 11, C represents 12, D represents 13, E represents 14 and F represents 15.

f) What is Unicode? How is it useful?
Definition:
Unicode is a new coding standard or character encoding system, promoted by Unicode Consortium. This new Unicode standard is adopted by all new platform. Unicode provides a unique number for every character. This unique number will be the same on all the platforms, programs and the languages.
Use:
1.
Unicode makes it possible to support the worldwide interchange, processing and display of the written text of the diverse languages.
2.
Due to this the support for various languages is provided.
3.
It is now possible to interchange data between different platforms.

g) Distinguish between ASCII and ISCII.
The following is the differentiation between ASCII and ISCII.
Basis
ASCII
ISCII
1. Full Form
Acronym for American Standard Code for Information Interchange
Acronym for Indian Standard Code for Information Interchange
2. Standard
This is an American Standard.
This is Indian Standard.
3. No. of Variations
Has two variations ASCII-7 and ASCII-8
Has only one variation.
4. No. of Characters
Has either 128 characters (in ASCII-7) or 256 characters (in ASCII-8)
Represents a larger set of characters
5. Representation Range
Has limited representation of characters.
Allows representation of English and Indian scripts simultaneously.
6. No. of Bits used
ASCII-7 used 7 bits and ASCII-8 used 8 bits to represent the characters
Uses 8 bits to represents the characters.
7. Supported Characters
Supports English and other Latin characters
Supports English and Indian Scripts

h) Do as directed :
Convert the Decimal number 781 to its Binary equivalent.
Convert Binary number 101101.001 to its decimal equivalent
Convert Octal number 321.7 into its Binary equivalent
Convert the Hexadecimal number 3BC into its Binary equivalent
Convert the Binary number 10011010.010101 to its Hexadecimal equivalent
Convert the Decimal number 345 into Octal number.
Convert the Decimal number 736 into Hexadecimal number.
Convert the Octal number 246.45 into Hexadecimal number.
Convert the Hexadecimal number ABF.C into Octal number.
Convert the Octal number 576 to Decimal.
Convert the Hexadecimal number A5C1 to Decimal.
Convresion of Decimal number 781 to its Binary equivalent.
Quotient
Remainder
{\dfrac{781}{2} = 390}
1
{\dfrac{390}{2} = 195}
0
{\dfrac{390}{2} = 97}
1
{\dfrac{97}{2} = 48}
1
{\dfrac{48}{2} = 24}
0
{\dfrac{24}{2} = 12}
0
{\dfrac{12}{2} = 6}
0
{\dfrac{6}{2} = 3}
0
{\dfrac{3}{2} = 1}
1
{\dfrac{1}{2} = 0}
1
∴ (781)10 = (1100001101)2
Conversion Binary number 101101.001 to its decimal equivalent.
101101.0012
=
(1 × 25)
+
(0 × 24)
+
(1 × 23)
+
(1 × 22)
+
(0 × 21)
+
(1 × 20)
+
(0 × 2-1)
+
(0 × 2-2)
+
1 × 2-3
=
32
+
0
+
8
+
4
+
0
+
1
+
0
+
0
+
0.125
= (45.125)10
∴ (101101.001)2 = (45.125)10
Convertion of Octal number 321.7 into its Binary equivalent
3
2
1
.
7
011
010
001
.
111
∴ (321.7)7 = (11010001.111)2
Note: Instead of 011010001.111, we’ve written this as 11010001.111 as zero in the beginning need not be considered.
Conversion of the Hexadecimal number 3BC into its Binary equivalent
3
B
C
0011
1011
1100
∴ (3BC)16 = (1110111100)2
Note: Instead of 001110111100, we’ve written this as 1110111100 as zero in the beginning need not be considered.
Conversion of the Binary number 10011010.010101 to its Hexadecimal equivalent
1001
1010
.
0101
0100
9
A
.
5
4
∴ (10011010)2 = (9A.54)16
Note The last column is added with two zeros and splitted as 0100 instead of simply 01 to ensure that there are four binaries at the end.
Convert the Decimal number 345 into Octal number.
Quotient
Remainder
{\dfrac{345}{8} = 43}
1
{\dfrac{43}{8} = 5}
3
{\dfrac{5}{8} = 0}
5
∴ (345)10 = (531)8
Conversion of the Decimal number 736 into Hexadecimal number.
Quotient
Remainder
{\dfrac{736}{16} = 46}
0
{\dfrac{46}{16} = 2}
14 = E
{\dfrac{2}{16} = 0}
2
∴ (736)10 = (2E0)16
Conversion of the Octal number 246.45 into Hexadecimal number.
Octal
2
4
6
.
4
5
3-Bit Binary
010
100
110
.
100
101
4-Bit Binary
0000
1010
0110
.
1001
0100
0
A
6
.
9
4
∴ (246.45)8 = (A6.94)16
Conversion of the Hexadecimal number ABF.C into Octal number.
A
B
F
.
C
4-Bit Binary
1010
1011
1111
.
1100
3-Bit Binary
101
010
111
111
.
110
Octal
5
2
7
7
.
6
∴ (ABF.C)16 = (5277.6)8
Conversion of the Octal number 576 to Decimal.
(576)8
=
(5 × 64)
+
(7 × 8)
+
(6 × 1)
=
320
+
56
+
6
=
382
∴ (576)8 = (382)10
Conversion of the Hexadecimal number A5C1 to Decimal.
(A5C1)16
=
(A × 163)
+
(5 × 162)
+
(C × 161)
+
(1 × 160)
=
(10 × 4096)
+
(5 × 256)
+
(12 × 16)
+
(1 × 1)
=
40960
+
1280
+
192
+
1
=
42433
∴ (A5C1)16 = (42433)10