Check sibling questions

Convert the following fractional binary number into decimal.

1100101.10110

 

Answer:

(1100101.10110) 2

=  1 x 2 6 + 1 x 2 5 + 0 x 2 4 + 0 x 2 3 + 1 x 2 2 + 0 x 2 1 + 1 x 2 0 + 1 x 2 -1 + 0 x 2 -2 + 1 x 2 -3 + 1 x 2 -4 + 0 x 2 -5

= 64 + 32 + 0 + 0 + 4 + 0 + 1 + 0.5 + 0 + 0.125 + 0.0625  + 0 

= (101.6875) 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.

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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.