Page 53 - Computer Science V2.0 Class 11

i. (101011100) to hexadecimal
2
added three 0s
0 0 0 1 0 1 0 1 1 1 0 0

1 5 C
(101011100) = (15C) 16
2
j. (F31) to binary
16
F 3 1
↓ ↓ ↓
1111 0011 0001
(F31) = (111100110001) 2
16
k. (474) to hexadecimal
8
Step1: Octal to Binary
4 7 4
↓ ↓ ↓
100 111 100
(100111100)
2
Step2: Binary to hexadecimal
0 0 0 1 0 0 1 1 1 1 0 0

1 3 C
= (13C) 16
Therefore (474) = (13C) 16
8
l. (C8E) to octal
16
Step1: Hexadecimal to Binary
C 8 E
↓ ↓ ↓
1100 1000 1110
(C8E) = (110010001110)
16 2
Step2: Binary to octal
1 1 0 0 1 0 0 0 1 1 1 0

6 2 1 6
= (6216) 8
Therefore (C8E) = (6216) 8
16
2.5.2 Fractional Numbers

In the previous section, we have discussed how to change the representation of a positive integer from one number
system to another. Let us now study the conversion of fractional numbers from one number system to another.
Decimal to Binary Conversion
To convert a decimal fraction between 0 and 1 (for example, (.25) and (0.40625) ) to binary, follow the steps given
10
10
below:
1. Multiply the fraction by 2.
2. Note the integer part of the product (0 or 1).
3. Multiply by two; the fraction left over after removing the integer part from the product.

Number Systems and Encoding Schemes 39