Page 64 - Computer Science V2.0 Class 11

Find octal representation of (9.7) , (5A.AF) , and (C4.98) .
16
16
16
Conversion of Octal Numbers to Hexadecimal
To convert an octal number to a hexadecimal number, first convert it to a binary number and then convert the binary
number to hexadecimal number.
Example 48: Convert (75.36) to a hexadecimal number
8
(75.36) 8
7 5 . 3 6
↓ ↓ ↓ ↓
111 101 011 110
Binary equivalent of (75.36) is (111101.011110)
8 2
two 0s added two 0s added

0 0 1 1 1 1 0 1 . 0 1 1 1 1 0 0 0

3 D . 7 8

Hexadecimal equivalent of (111101.011110) is (3D.78) 16
2

1. Write binary and octal equivalents for the following hexadecimal digits:
F, A, 5, C
2. Find hexadecimal representation of (10.5) , (32.6) and (40.3) .
8
8
8

Do the following conversions:
a. (10011.01) to decimal
2
b. (C25.D2) to decimal
16
c. (157.25) to decimal
8
d. (0.341) to hexadecimal
10
Ans:
a. (10011.01) to decimal number.
2
Face Value 1 0 0 1 1 . 0 1
0
Place value 2 4 2 3 2 2 2 1 2 . 2 –1 2 –2
4
3
2
–1
0
1
= 1 × 2 + 0 × 2 + 0 × 2 + 1 × 2 + 1 × 2 + 0 × 2 + 1 × 2 –2
= 16 + 0 + 0 + 2 + 1 + 0 + 1
4
= 19 + 0.25
= 19.25
= (10011.01) = (19.25) 10
2
b. (C25.D2) to decimal number.
16
Face Value C 2 5 . D 2
–1
0
1
2
Place value 16 16 16 . 16 16 –2
= C × 16 + 2 × 16 + 5 × 16 + D × 16 + 2 × 16 –2
1
0
–1
2
= 12 × 256 + 2 × 16 + 5 × 1 + 13 + 2
16 256
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