NCERT Solutions: Encoding Schemes and Number System
Q1: Write base values of binary, octal, and hexadecimal number systems.
Ans: The base value of the binary system is 2, the octal system is 8, and the hexadecimal system is 16.
Q2: Give the full form of ASCII and ISCII.
Ans: ASCII stands for American Standard Code for Information Interchange, and ISCII stands for Indian Script Code for Information Interchange.
Q3: Try the following conversions.
(i) (514)8 = (?)10
(ii) (220)8 = (?)2
(iii) (76F)16 = (?)10
(iv) (4D9)16 = (?)10
(v) (11001010)2 = (?)10
(vi) (1010111)2 = (?)10
Ans:
(i) (514)₈ is equal to (332)₁₀.
(ii) (220)₈ is represented as (10010000)₂.
(iii) (76F)₁₆ converts to (1903)₁₀.
(iv) (4D9)₁₆ is equivalent to (1241)₁₀.
(v) (11001010)₂ corresponds to (202)₁₀.
(vi) (1010111)₂ converts to (87)₁₀.
Q4: Do the following conversions from decimal to other number systems.
(i) (54)10 = (?)2
(ii) (120)10 = (?)2
(iii) (76)10 = (?)8
(iv) (889)10 = (?)8
(v) (789)10 = (?)16
(vi) (108)10 = (?)16
Ans:
(i) (54)₁₀ is (110110)₂.
(ii) (120)₁₀ is (1111000)₂.
(iii) (76)₁₀ is (114)₈.
(iv) (889)₁₀ is (1571)₈.
(v) (789)₁₀ is (315)₁₆.
(vi) (108)₁₀ is (6C)₁₆.
Q5: Express the following octal numbers into their equivalent decimal values.
(i) 145
(ii) 6760
(iii) 455
(iv) 10.75
Ans:
(i) (145)₈ equals (101)₁₀.
(ii) (6760)₈ converts to (3568)₁₀.
(iii) (455)₈ is the same as (301)₁₀.
(iv) (10.75)₈ corresponds to (8.953125)₁₀.
Q6: Express the following decimal numbers into hexadecimal numbers.
(i) 548
(ii) 4052
(iii) 58
(iv) 100.25
Ans:
(i) (548)₁₀ is (224)₁₆.
(ii) (4052)₁₀ is (FD4)₁₆.
(iii) (58)₁₀ is (3A)₁₆.
(iv) (100.25)₁₀ is (64.4)₁₆.
Q7: Express the following hexadecimal numbers into equivalent decimal numbers.
(i) 4A2
(ii) 9E1A
(iii) 6BD
(iv) 6C.34
Ans:
(i) (4A2)₁₆ equals (1186)₁₀.
(ii) (9E1A)₁₆ converts to (40474)₁₀.
(iii) (6BD)₁₆ is equivalent to (1725)₁₀.
(iv) (6C.34)₁₆ corresponds to (108.203125)₁₀.
Q8: Convert the following binary numbers into octal and hexadecimal numbers.
(i) 1110001000
(ii) 110110101
(iii) 1010100
(iv) 1010.1001
Ans:
(i) (1110001000)₂ is (1610)₈ and (388)₁₆.
(ii) (110110101)₂ converts to (665)₈ and (1B5)₁₆.
(iii) (1010100)₂ is (124)₈ and (54)₁₆.
(iv) (1010.1001)₂ corresponds to (12.44)₈ and (A.9)₁₆.
Q9: Write binary equivalent of the following octal numbers.
(i) 2306
(ii) 5610
(iii) 742
(iv) 65.203
Ans:
(i) (2306)₈ converts to (10011000110)₂.
(ii) (5610)₈ is (101110001000)₂.
(iii) (742)₈ corresponds to (111100010)₂.
(iv) (65.203)₈ is equivalent to (110101.010000011)₂.
Q10: Write binary representation of the following hexadecimal numbers.
(i) 4026
(ii) BCA1
(iii) 98E
(iv) 132.45
Ans:
(i) (4026)₁₆ is (100000000100110)₂.
(ii) (BCA1)₁₆ corresponds to (1011110010100001)₂.
(iii) (98E)₁₆ is (100110001110)₂.
(iv) (132.45)₁₆ converts to (100110010.010001012)₂.
Q11: How does the computer process the following text using a 7-bit ASCII code?
How does computer understand the following text? (hint: 7 bit ASCII code).
(i) HOTS
(ii) Main
(iii) CaSe
Ans:
(i) HOTS → 1001000100111110101001010011.
(ii) Main → 1001101110000111010011101110.
(iii) CaSe → 1000011110000110100111100101.
Q12: The hexadecimal number system uses 16 literals (0-9, A-F). Write down its base value.
Ans: The base value of the hexadecimal system is 16.
Q13: Let X be a number system having B symbols only. Write down the base value of this number system.
Ans: The base value of this system is B, as the number of unique symbols determines the base, similar to how binary has a base of 2, octal has 8, and decimal has 10.
Q14: Write the equivalent hexadecimal and binary values for each character of the phrase given below.
'' हम सब एक"
Ans:
ह → 0939, 100100111001
म → 092E, 100100101110
स → 0938, 100100111000
ब → 092C, 100100101100
ए → 090F, 100100001111
क → 0915, 100100010101
Q15: What is the advantage of preparing a digital content in Indian language using UNICODE font?
Ans: The primary advantage of UNICODE is that it eliminates the need for additional font installation, as the system automatically renders these fonts.
Q16: Explore and list the steps required to type in an Indian language using UNICODE.
Ans:
Step 1: Write characters, words, or sentences in the desired Indian language.
Step 2: UNICODE assigns a unique value to each character, making it readable by machines.
Step 3: The system converts the UNICODE characters into machine-readable binary form.
Q17: Encode the word 'COMPUTER' using ASCII and convert the encode value into binary values.
Ans:
C → 67, 1000011
O → 79, 1001111
M → 77, 1001101
P → 80, 1010000
U → 85, 1010101
T → 84, 1010100
E → 69, 1000101
R → 82, 1010010
Binary representation of COMPUTER: 10000111001111100110110100001010101101010010001011010010.
