Page 60 - Computer Science V2.0 Class 11

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
8
10
↓
Recurring digit (6)

Example 32: Convert (705.81) to its equivalent hexadecimal number, accurate to three places after the radix point.
10
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)
10 16

Find hexadecimal representation of (0.25) , (0.75) and (0.125) .
10 10 10

Conversion of Hexadecimal Fractions to Decimal

To convert an hexadecimal fraction to decimal, we use place values (base 16) and follow the following steps:
1. Write the hexadecimal 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 33: Convert (0.A6) to its equivalent decimal number.
16
Face Value 0 . A 6
–1
Place value 16 16 –2
–1
= A × 16 + 6 × 16 –2
= A + 6
16 256

= 10 + 6
16 256
= 0.625 + 0.023

= (0.648) 10

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