Page 51 - Computer Science Class 11 Without Functions
P. 51
Example 15: Convert (0.3) to binary.
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Fraction part Integer part
0.3 × 2 = 0.6 0.6 0
0.6 × 2 = 1.2 0.2 1
0.2 × 2 = 0.4 0.4 0
0.4 × 2 = 0.8 0.8 0
0.8 × 2 = 1.6 0.6 1
0.6 × 2 = 1.2 0.2 1
0.2 × 2 = 0.4 0.4 0
0.4 × 2 = 0.8 0.8 0
0.8 × 2 = 1.6 0.6 1
(0.3) = (0.010011001)
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Recurring digits
So, we can write, (0.3) as (0.0 1001 1001) if 9-bit accuracy of the fraction part is required, (0.3) as (0.0 1001
10 2 10
1001 100) if 12-bit accuracy of the fraction part is required, and (0.3) as (0.0 1001 1001 1001 1001 1001) if 21-bit
2 10 2
accuracy of the fraction part is required.
Similarly, the binary equivalent of (0.8) is (0.110011001100110011) to 18 decimal places as the digits '1100' are
10
2
being repeated.
The same method will apply when the fraction is represented as (p/q) . Let us illustrate it on 3/7 .
10
10
Example 16: Convert 3/7 to an equivalent binary number.
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Fraction part Integer part
(3/7) × 2 = 6/7 6/7 0
(6/7) × 2 = 12/7 5/7 1
(5/7) × 2 = 10/7 3/7 1
(3/7) × 2 = 6/7 6/7 0
(6/7) × 2 = 12/7 5/7 1
(5/7) × 2 = 10/7 3/7 1
3/7 = (0.011011) Recurring digits
10
2
To obtain the binary representation of a decimal number having an integer and the fractional part, then apply the
following steps:
1. Convert the integer part to an equivalent binary number (say, a)
2. Convert the fraction part between 0 and 1 to an equivalent binary number between 0 and 1 (say, b).
3. Write the binary representation of the integer part, followed by the binary representation of the fraction part.
Example 17: Convert (101.25) to its equivalent binary number.
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Whole number part - 101
2 101 Remainder
2 50 1
2 25 0
2 12 1
= (1100101)
2 6 0 2
2 3 0
2 1 1
0 1
Number Systems and Encoding Schemes 49

