Page 55 - Computer Science Class 11 Without Functions
P. 55
Example 27: Convert (902.82) to its octal equivalent, accurate to three places after the radix point.
10
8 902 Remainder
8 112 6
8 14 0
= (1606)
8 1 6 8
8 0 1
Fraction part Integer part
0.82 × 8 = 6.56 0.56 6
0.56 × 8 = 4.48 0.48 4 =(.643) 8
0.48 × 8 = 3.84 0.84 3
(902.82) = (1606.643) 8
10
Find octal representation of (3.25) , (20.50) and (32.125) .
10
10
10
Conversion of Fractions from Octal to Decimal
To convert an octal fraction to decimal, we use place values (base 8) and follow the following steps:
1. Write the octal number.
2. Below each digit, write the place value of each digit position.
3. Multiply the face value of each digit with its place value.
4. Add all values obtained in step 3 to get the decimal number.
Example 28: Convert (0.412) to decimal
8
Face Value 0 . 4 1 2
Place Value 0 8 –1 8 –2 8 –3
= 4 × 8 + 1 × 8 + 2 × 8 –3
–1
–2
= 4 + 1 + 1
8 64 512
= 0.5 + 0.015625 + 0.001953125
= (0.517578125) 10
Example 29: Convert (1606.643) to decimal
8
Face Value 1 6 0 6 . 6 4 3
Place Value 8 3 8 2 8 1 8 0 8 –1 8 –2 8 –3
–2
2
–1
3
1
0
= 1 × 8 + 6 × 8 + 0 × 8 + 6 × 8 + 6 × 8 + 4 × 8 + 3 × 8 –3
= 512 + 384 + 0 + 6 + 0.75 + 0.0625 + 0.00585
= (902.81835) 10
Find decimal representation of (0.2) , (0.4) and (0.7) .
8 8 8
Number Systems and Encoding Schemes 53

