Data Representation Class 11 CS Sumita Arora Solution

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Q1. Convert the following binary numbers to decimal :

(a) 1010

(b) 111010

(c) 101011111

 

Answer :-

 

(a)

 

1	0	1	0
23	0	21	0	(1010)2=(10)10

 

(b)

 

1	1	1	0	1	0
25	24	23	0	22	0	(111010)2=(60)10

 

(c)

 

1	0	1	0	1	1	1	1	1
28	0	26	0	24	23	22	21	1	(101011111)2=(351)10

 

 

 

Q2. Convert the following binary numbers to decimal :

(a) 1100

(b) 10010101

(c) 11011100

 

Answer :-

 

(a)

 

1	1	0	0
23	22	0	0	(1100)2=(12)10

 

(b)

 

1	0	0	1	0	1	0	1
27	0	0	24	0	22	0	1	(10010101)2 = (149)10

 

(c)

 

1	1	0	1	1	1	0	0
27	26	0	24	23	22	0	0	(1101110)2 = (110)10

 

 

Q3. Convert the following decimal numbers to binary :

(a) 23

(b) 100

(c) 145

 

Answer :-

 

(a)

 

Division	Remainder (R)
23 / 2 = 11	1
11 / 2 = 5	1
5 / 2 = 2	1
2/ 2 = 1	0
1/ 2 = 0	1

(23)10=(10111)2

 

(b)

Division	Remainder
100/2=50	0
50/2=25	0
25/2=12	1
12/2=6	0
6/2=3	0
3/2=1	1
1/2=0	1

(100)10=(1100100)2

 

(c)

 

Division	Remainder
145/2=72	1
72/2=36	0
36/2=18	0
18/2=9	0
9/2=4	1
4/2=2	0
2/2=1	0
1/2=0	1

(145)10=(10010001)2

 

 

Q4. Convert the following decimal numbers to binary:

(a) 19

(b) 121

(c) 161

 

Answer :-

 

(a)

division	Remainder
19/2=9	1
9/2=4	1
4/2=2	0
2/2=1	0
1/2=0	0

(19)10=(00011)2

 

(b)

Division	Remainder
121/2=60	1
60/2=30	0
30/2=15	0
15/2=7	1
7/2=3	1
3/2=1	1
1/2=0	1

(121)10=(1111001)2

 

 

(C)

Division	Remainder
161/2=80	1
80/2=40	0
40/2=20	0
20/2=10	0
10/2=5	0
5/2=2	1
2/2=1	0
1/2=0	1

(161)10=(10100001)2

 

 

Q5. Convert the following hexadecimal numbers to binary:

(a) A6

(b) A07

(c) 7AB4

 

Answer :-

 

(a)

A	6
1010	0110

(A6)16=(10100110)2

 

(b)

A	0	7
1010	0000	0111

(A07)16=(101000000111)2

 

(c)

7	A	B	4
0111	1010	1011	0100

(7AB4)16=(0111101010110100)2

 

 

Q6. Convert the following hexadecimal numbers to binary:

(a) BE

(b) BC9

(c) 9BC8

 

Answer :-

 

(a)

B	E
1011	1110

(BE)16=(10111110)2

 

(b)

B	C	9
1011	1100	1001

(BC9)16=(101111001001)2

 

(c)

9	B	C	8
1001	1011	1100	1000

(9BC8)16=(1001101111001000)2

 

 

Q7. Convert the following binary numbers to hexadecimal:

(a) 10011011101

(b) 1111011101011011

(c) 11010111010111

 

Answer :-

 

(a)

0100	1101	1101
4	D	D

(10011011101)2=(4DD)16

 

(b)

1111	0111	0101	1011
F	7	5	B

(1111011101011011)2 = (F75B)16

 

(c)

0011	0101	1101	0111
3	5	D	7 (11010111010111)2 = (35D7)16

 

 

Q8. Convert the following binary numbers to hexadecimal:

(a) 1010110110111

(b) 10110111011011

(c) 1111101110101111

 

Answer :-

 

(a)

0001	0101	1011	0111
1	5	B	7 (0001010110110111)2 = (15B7)16

(b)

0010	1101	1101	1011
2	D	D	B (10110111011011)2 = (2DDB)16

(c)

1111	1011	1010	1111
F	B	A	F (1111101110101111)2 = (FBAF)16

 

Q9. Convert the following hexadecimal numbers to decimal:

(a) A6

(b) A13B

 

Answer :-

 

(a)

A6 = (10 * 16¹) + (6 * 16⁰)

A6 = (10 * 16) + (6 * 1)

A6 = 160 + 6

A6 = 166 (in decimal number)

(B)

A13B= (10 * 16^3) + (1 * 16^2) + (3 * 16^1) + (11 + 16^0)

A13B = (10 * 4096) + (1 * 256) + (3 * 16) + (11 *1 )

A13B = 41275 (in decimal number)

 

 

Q10. Convert the following hexadecimal numbers to decimal:

(a) E9
(b) 7 CA3

 

Answer :-

 

(A)

E9 is a hex number

E9 = (14 * 16¹) + (9 * 16⁰)

E9 = (14 * 16) + (9 * 1)

E9 = 224 + 9

E9 = 233 (in decimal number)

(B)

7CA3 is a hex number

7CA3 = (7 * 16³) + (12 * 16²) + (10 * 16¹) + (3 *1)

7CA3 = (7 * 4096) + (12 * 256) + (16*10) + (3)

7CA3 = 31915

7CA3 = 31915 (in decimal number)

 

Q11. Convert the following decimal numbers to hexadecimal:

(a) 132
(b) 2352

 

Answer :-

 

(a)

Division	Remainder
132/16=8	4
8/16=0	8 (132)10 = (84)16

(b)

Division	Remainder
2352/16=147	0
147/16=9	3
9/16=0	9 (2352)10 = (930)16

 

Q12. Convert the following decimal numbers to hexadecimal:

(a) 206
(b) 3619

 

Answer :-

 

(a)

Division	Remainder
206/16=12	14
12/16=0	12 (206)10 = (CE)16

(b)

Division	Remainder
3619/16=226	3
226/16=14	2
14/16=0	14 (E) (3619)10 = (E23)16

 

13. Convert the following hexadecimal numbers to octal :

(a) 38 AC

(b) 7FD6

(c) ABCD

 

Answer :-

 

(a)
Hexadecimal Number = 38AC

3              8              A              C
0011              1000              1010              1100

(38AC)16=(0011100010101100)2

 

(b)
Hexadecimal Number = 7FD6

7              F              D              6

0111              1111              1101              0110

 

(7FD6)₁₆ = (0111111111010110)₂

 

(c)

Hexadecimal Number = ABCD

(ABCD)₁₆ = (1010101111001101)₂

 

 

14. Convert the following octal numbers to binary:

(a) 123

(b) 3527

 

Answer :-

(a)

(123)₈ = (1010011)₂

 

Octal number is 123	1	2	3
Binary	001	010	011

 

(b

(3527)₈ = (11101010111)₂

 

Octal number is 3527	3	5	2	7
Binary	011	101	010	111

15. Convert the following octal numbers to binary:

(a) 7642

(b) 7015
(c) 3576

 

Answer :-

 

(a)

(7642)₈ = (111110100010)₂

 

Conversion table:Octal	Binary
0	000
1	001
2	010
3	011
4	100
5	101
6	110
7	111

 

the given octal number is 7642:Octal	7	6	4	2
Binary	111	110	100	010

 

(b)

(7015)₈ = (111000001101)₂

 

Octal number is 7015	7	0	1	5
Binary	111	000	001	101

 

(c)

(3576)₈ = (11101111110)₂

 

Octal number is 3576	3	5	7	6
Binary	011	101	111	110

16. Convert the following binary numbers to octal:

(a) 111010

(b) 110110101
(c) 1101100001

 

Answer :-

 

(a)

 

Binary number :- 111010

111              010
7              2

111010₂=72₈

(b)

 

Binary number :- 110110101

(110110101)₂ = (665)₈

 

Conversion table:Octal	Binary
0	000
1	001
2	010
3	011
4	100
5	101
6	110
7	111

 

Binary	110	110	101
Octal number	6	6	5

 

(c)

(1101100001)₂ = (1541)₈

 

Binary	1	101	100	001
Octal number	1	5	4	1