Page 61 - Computer Science Class 11 Without Functions
P. 61
0
–1
1
2
3
4
= 1 × 2 + 0 × 2 + 0 × 2 + 1 × 2 + 1 × 2 + 0 × 2 + 1 × 2 –2
1
= 16 + 0 + 0 + 2 + 1 + 0 +
4
= 19 + 0.25
= 19.25
= (10011.01) = (19.25) 10
2
b. (C25.D2) to decimal number.
16
Face Value C 2 5 . D 2
–1
1
0
2
Place value 16 16 16 . 16 16 –2
1
0
2
–1
= C × 16 + 2 × 16 + 5 × 16 + D × 16 + 2 × 16 –2
13 2
= 12 × 256 + 2 × 16 + 5 × 1 + +
16 256
= 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
2
–1
0
1
= 1 × 8 + 5 × 8 + 7 × 8 + 2 × 8 + 5 × 8 –2
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.
Number Systems and Encoding Schemes 59

