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

Do as directed:

(a) Convert the Decimal number 781 to its Binary equivalent.

(b) Convert Binary number 101101.001 to its decimal equivalent

(c) Convert Octal number 321.7 info its Binary equivalent

 

Answer:

(a) 781 10 to its binary equivalent

Converting Decimal 781 (Base 10) into Binary (Base 2) - Teachoo.jpg

Therefore, 781 10 = 1100001101 2

Explanation:

  • Repeatedly divide the decimal number by 2 until the quotient becomes 1 and record all the remainders. 
  • The remainders should be written bottom to upwards to get the binary equivalent of the decimal number.

(b) 101101.001 2 to its decimal equivalent

        101101.001 = 1 x 2 5 + 0 x 2 4 + 1 x 2 3 + 1 x 2 2 + 0 x 2 1 + 1 x 2 0 + 0 x 2 -1 + 0 x 2 -2 + 1 x 2 -3

                            = 32 + 0 + 8 + 4 + 0 + 1 + 0 + 0 + 0.125

                = 45.125 10

Explanation:

  • To obtain the decimal equivalent of a binary number, individual digits of binary number should be multiplied by powers of 2 starting with the rightmost digit multiplied by 2 0 , second last digit multiplied by 2 1 , third last digit multiplied by 2 2 and so on up to the leftmost digit. 
  • For digits after the decimal point, the leftmost digit should be multiplied by 2 -1 and the next digit by 2 -2 and so on up to the rightmost digit.

(c)    321.7 8 to its binary equivalent

         

3

2

1

7

011

010

001

111

      Therefore, 321.7 8 = 11010001.111 2

Explanation:

  • To obtain binary equivalent of an octal number, individual digits of octal number should be converted to binary in groups of three digits as given in the table below.

Decimal, Binary And Octal Number System Full Comparison - Teachoo.jpg

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Transcript

Converting Decimal 781 (Base 10) into Binary (Base 2) Decimal, Binary And Octal Number System – Full Comparison

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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.