Page 75 - Computer Science V2.0 Class 11

vi.

Digits 1 0 1 0 1 1 1
Position 6 5 4 3 2 1 0
Weight 2 6 2 5 2 4 2 3 2 2 2 1 2 0
Therefore,
3
2
1
6
5
4
Decimal number = 1×2 + 0×2 +1×2 +0×2 +1×2 +1×2 +1×2 0
= 64 +16 + 4+ 2 +1
= (87) 10
4. Do the following conversions from decimal number to other number systems.

i. (54) = (?) 2
10
ii. (120) = (?)
10
2
iii. (76) = (?)
8
10
iv. (889) = (?) 8
10
v. (789) = (?) 16
10
vi. (108) = (?) 16
10
Ans. i.
2 54
2 27 0
2 13 1
2 6 1
2 3 0
2 1 1

2 0 1

= (110110) 2
ii.

2 120
2 60 0
2 30 0

2 15 0
2 7 1

2 3 1
2 1 1
0 1
= (1111000) 2
iii.
8 76

8 9 4
8 1 1

0 1
= (114) 8

Number Systems and Encoding Schemes 61