Page 78 - Computer Science V2.0 Class 11

iv.
16 100
16 6 4

0 6

0.25 × 4 = 4
= (100.25) = (64.4) 16
10
7. Express the following hexadecimal numbers into equivalent decimal numbers.
i. 4A2
ii. 9E1A
iii. 6BD
iv. 6C.34
Ans. i.
Digits 4 A 2
Position 2 1 0
Weight 16 2 16 1 16 0
2
1
Decimal number = 4 × 16 + A × 16 + 2 × 16 0
= 4 × 256 + 10 × 16 + 2 × 1
= (1186) 10
ii.
Digits 9 E 1 A

Position 3 2 1 0
Weight 16 3 16 2 16 1 16 0
1
3
2
Decimal number = 9 × 16 + E × 16 + 1 × 16 + A × 16 0
= 9 × 4096 + 14 × 256 + 1 × 16 + 10 × 1
= (40474) 10
iii.
Digits 6 B D
Position 2 1 0
Weight 16 2 16 1 16 0

Decimal number = 6 × 16 + B × 16 + D × 16 0
1
2
= 6 × 256 + 11 × 16 + 13 × 1
= (1725) 10
iv.
Digits 6 C 3 4
Position 1 0 -1 -2
Weight 16 1 16 0 16 -1 16 -2
Decimal number = 6 × 16^1 + C × 16^0 + 3 × 16^-1 + 4 × 16^-2
= 96 + 12 × 1 + 0.1875 + 0.015625 [as C = 12 in base 16]
= (108.203125) 10
8. Convert the following binary numbers into octal and hexadecimal numbers.
i. 1110001000
ii. 110110101
iii. 1010100
iv. 1010.1001

64 Touchpad Computer Science (Ver. 2.0)-XI