Q1. Convert the following binary numbers to decimal :

(a) 1010

(b) 111010

(c) 101011111

(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

(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

(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

(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

(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

(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

(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

(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

(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

(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

(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

(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

(a)

3              8              A              C
0011              1000              1010              1100

(38AC)16=(0011100010101100)2

(b)

7              F              D              6

0111              1111              1101              0110

(7FD6)16 = (0111111111010110)2

(c)

(ABCD)16 = (1010101111001101)2

14. Convert the following octal numbers to binary:

(a) 123

(b) 3527

(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

(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

(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

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