Page 56 - Computer Science Class 11 Without Functions
P. 56
Conversion of Decimal Fractions to Hexadecimal
To convert fractional numbers in a decimal number system to hexadecimal, the steps are as follows:
1. Multiply the fractional part by 16.
2. Note the integer part after multiplication by 16.
3. Multiply only the fractional part obtained in step 1 by 16.
4. In the case of terminating fractions, repeat steps 2 and 3 till the fractional part becomes zero. However, in the case
of non-terminating fractions, repeat steps 2 and 3 up to the recurring integer part. Examples 30 and 31 illustrate
the conversion of terminating and non-terminating fractions.
5. The integer part, from top to bottom forms the hexadecimal number.
Example 30: Convert (0.25) to its equivalent hexadecimal number.
10
Integer part
0.25 × 16 = 4.0 4
0.0 × 16 = 0 0
= (0.40)
16
Example 31: Convert (0.65) to its equivalent hexadecimal number.
10
Fraction part Integer part
0.65 × 16 = 10.4 0.4 10 → A
0.4 × 16 = 6.4 0.4 6
0.4 × 16 = 6.4 0.4 6
0.4 × 16 = 6.4 0.4 6
(0.65) = (0.A6) 16
10
(0.65) = (0.A666…) = (0.A6) 8
10
8
↓
Recurring digit (6)
Example 32: Convert (705.81) to its equivalent hexadecimal number, accurate to three places after the radix
10
point.
16 705 Remainder
16 44 1
16 2 12 → C (2C1) 16
0 2
Fraction part Integer part
0.81 × 16 = 12.96 0.96 12 → C
0.96 × 16 = 15.36 0.36 15 → F (CF5) 16
0.36 × 16 = 5.76 0.76 5
(705.81) = (2C1.CF5) 16
10
Find hexadecimal representation of (0.25) , (0.75) and (0.125) .
10
10
10
54 Touchpad Computer Science-XI

