Check sibling questions
Computer Science - Class 11
Chapter 2 Class 11 - Encoding Schemes and Number System

Do as directed.

(a) Convert the Hexadecimal number 3BC into its Binary equivalent

(b) Convert the Binary number 10011010.010101 to its Hexadecimal equivalent.

(c) Convert the Decimal number 345 into Octal number

 

Answer:

(a) 3BC 16 to its binary equivalent

       

3

B

C

0011

1011

1100

     

    Therefore, 3BC 16 = 001110111100 2

Explanation:

  • To obtain the binary equivalent of a hexadecimal number, individual digits of the hexadecimal number should be converted to binary in groups of four digits as given in the table below.

Decimal, Binary And Hexadecimal Numbers - Full Comparison - Teachoo.jpg

 

 

(b) 10011010.010101 2 to its hexadecimal equivalent

       

1001

1010

0101

01 00

9

A

5

4

      Therefore, 10011010.010101 2 = 9A.54 16

 

Explanation:

  • To obtain the Hexadecimal equivalent of a binary number, digits of binary number should be divided into groups of four digits starting from the rightmost digit for the integer part and starting from the leftmost digit for the fractional part. 
  • Convert each group of 4 digits to one hexadecimal digit as given in the table below.
  • Note: 1,2 or 3 zeroes can be added before the leftmost digit or after the rightmost digit to make a complete group of 4 bits.

Decimal, Binary And Hexadecimal Numbers - Full Comparison - Teachoo.jpg

(c) 345 10 to its octal equivalent

Converting Decimal 345 (Base 10) into Octal (Base 8) - Teachoo.jpg

      

Therefore, 345 10 = 531 8

 

Explanation:

  • Repeatedly divide the decimal number by 8 until the quotient becomes less than 8 and record all the remainders. 
  • The remainders should be written bottom to upwards to get the octal equivalent of the decimal number.

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.