NCERT Solutions Class 11 Computer Science Chapter 2 Encoding Schemes and Number System

Question 1:  Write base values of binary, octal and hexadecimal number system.

Answer:

NUMBER SYSTEMBASE VALUE
Binary number system2
Octal number system8
hexadecimal number system16

Question 2:  Give full form of ASCII and ISCII.

Answer:

  • The full form of ASCII is American Standard Code for Information
  • The full form of ISCII is Indian Script Code for Information Interchange.

Question 3:   Try the following conversions.

(i) (514)8 = (?)10         (iv) (4D9)16 = (?)10

(ii) (220)8 = (?)2          (v) (11001010)2 = (?)10

(iii) (76F)16 = (?)10    (vi) (1010111)2 = (?)10

Answer:

  • (514)8 = (?)10
Digits51   4
Position21   0
Weight828180

Therefore,

                  Decimal number = 5×82 + 1×8+ 4×8

                                      = 5×64 + 1×8 + 4× 1

                                      = 320 + 8 + 4

= (332)10

  • (220)8 = (?)2
Octal Digits22   0
Binary value    (3 bits)010010   000

Therefore,

                  Binary number = (010010000)2

  • (76F)16 = (?)10
Digits76  F(15)
Position21   0
Weight162161160

Therefore,

Decimal number = 7×162 + 6×16+ F×16

                         = 7×256 + 6×16 + F× 1

                                      = 1792 + 96 + 15

                                         = (1903)10

  • (4D9)16 = (?)10
Digits4D  9
Position21   0
Weight162161160

Therefore,

Decimal number = 4×162 + 13×16+ 9×16

                         = 4×256 + 13×16 + 9× 1

                                      = 1024 + 208 + 9

                                         = (1241)10

  • (11001010)2 = (?)10
Digits11001010
Position76543210
Weight2726252423222120

 Therefore,

Decimal number = 1×27+ 1×26+0×25 +0×24 +1×23 +0×22 +1×21 +0×20

                         = 128+64 +8 + 2

                                      = (202)10

  • (1010111)2 = (?)10
Digits1010111
Position6543210
Weight26252423222120

Therefore,

Decimal number = 1×26+ 0×25+1×24 +0×23 +1×22 +1×21 +1×20

                         = 64 +16 + 4+ 2 +1

                                      = (87)10

Question 4: Do the following conversions from decimal number to other number systems.

(i) (54)10 = (?)2          (iv) (889)10 = (?)8

(ii) (120)10 = (?)2        (v) (789)10 = (?)16

(iii) (76)10 = (?)8        (vi) (108)10 = (?)16

Answer:

Question 5: Express the following octal numbers into their equivalent decimal numbers.

(i) 145

(ii) 6760

(iii) 455

(iv) 10.75

Answer:

(i) 145

Digits14   5
Position21   0
Weight828180

Therefore,

 Decimal number = 1×82 +4×8+ 5×8

                                      =1×64 + 4×8 + 5× 1

                                      =64 + 32 + 5

= (101)10

(ii) 6760

Digits676  0
Position321  0
Weight838281    80

Therefore,

Decimal number = 6×83 +7×82 +6×8+ 0×8

                                      =6×512 + 7×64 +6×8 + 0× 1

                                      =3072 + 448 + 48+0

= (3568)10

(i) 455

Digits45   5
Position21   0
Weight828180

Therefore,

Decimal number = 4×82 +5×8+ 5×8

                                      =4×64 + 5×8 + 5× 1

                                      =256 + 40 + 5

= (301)10

(iv) 10.75

Digits10   75
Position10   -1-2
Weight81808-18-2

 Therefore,

Decimal number = 1×81+0×80+7×8-1+5×8-2 

                                        =1×8+0×1+7×0.125+5×0.015625

                                        =8+0+0.875+0.078125

= (8.953125)10

Question 6:  Express the following decimal numbers into hexadecimal numbers. (i) 548 (ii) 4052 (iii) 58 (iv) 100.25


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