Page 65 - Computer Science V2.0 Class 11

= 3072 + 32 + 5 + 0.812 + 0.007
= 3109.819
= (C25.D2) = (3109.819) 10
16
c. (157.25) to decimal number.
8
Face Value 1 5 7 . 2 5
Place value 8 2 8 1 8 0 8 -1 8 -2

0
1
2
= 1 × 8 + 5 × 8 + 7 × 8 + 2 × 8 + 5 × 8 -2
-1
2
= 64 + 40 + 7 + + 5
8 64
2
= 111 + + 5
8 64
= 111 + 0.25 + 0.07
= 111.328
Hence, (157.25) = (111.328) 10
8
d. (0.341) to hexadecimal till 3 digits after the radix point.
10
Fraction part Integer part
0.341 × 16 = 5.456 0.456 5

0.456 × 16 = 7.296 0.296 7
0.296 × 16 = 4.736 0.736 4
(0.341) = (.574) 16
10
2.6 Encoding Schemes

We have studied various number systems that enable us to deal with numeric data. Besides numbers, computers also
deal with other forms of data like the text of characters, speech, images, and signals from various equipment such
as ECG, MRI, radars, satellites, and mobiles. However, besides numbers, the text is the most common form of input
to computers and the most common form of output produced by computers. As the text comprises characters, we
will study the representation of characters in this section. As the computer needs to distinguish between different
characters, a unique code is assigned for each character. A mapping of the characters to their unique codes is called an
encoding scheme. When a key is pressed on the keyboard, it is internally mapped to a unique code.
Several encoding schemes have evolved over the years, for example, ASCII and UNICODE. India has also developed the
Indian Script Code for Information Interchange (ISCII)—a coding scheme for representing characters in various writing
systems in India.

2.6.1 American Standard Code for Information Interchange (ASCII)
This is the most commonly used encoding scheme used to encode characters in the English language. The ASCII
(pronounced as askee) code is a 7-bit code. So, it can only codify 2 =128 different characters. The Extended ASCII is
7
an eight-bit code that includes 256 characters and retains most of the ASCII codes. Extended Binary Coded Decimal
Interchange Code is an 8-bit code developed by IBM for its mainframe computers.
Table 2.10 shows characters and their ASCII codes, expressed in decimal numbers. Note that ASCII code for the
uppercase alphabet A is 65, and subsequent alphabets are assigned incrementally higher values. Thus, ASCII codes for
the characters B, C, D, … are 66, 67, 68, … . Similarly, ASCII code for the lowercase alphabet a is 97, and subsequent
alphabets are assigned incrementally higher values. Thus, ASCII codes for the characters b, c, d, … are 98, 99, 100, … .
and ASCII code for the digit 0 is 48, and subsequent digits are assigned incrementally higher values. Thus, ASCII codes
for the digits 1, 2, 3, … are 49, 50, 51, … .

Number Systems and Encoding Schemes 51