Please:- Rotate Your mobile for better Experience of Solution 

 

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

 

 


10 Comments

You can help us by Clicking on ads. ^_^
Please do not send spam comment : )

Post a Comment

You can help us by Clicking on ads. ^_^
Please do not send spam comment : )

Previous Post Next Post