Question

convert fraction decimal number 14/13 to acorrectly rounded binary number with 8 digits.

Answer 1

Convert decimal to binary using division method

1. Division method is used to convert only integer part of a decimal number to its equivalent in binary number system.

2. In this method the integer part of the decimal number is continuously divided until we reach a stage where the quotient becomes zero.

3. The reminder that we obtain at each division iteration becomes the value of the weights or the digits in the binary number system.

4. The reminders that we obtain are taken from the last step to first step i.e. the last reminder obtained during the division iteration is the most significant digit (MSD) and the first reminder the we obtained is the least significant digit in the binary number system.

5. You will understand the procedure better with the following illustrative example.

Step1:

Convert (14)₁₀ decimal number to binary number (?)₂ using division method

1st Division Iteration

Divide 14 by 2

14 ÷ 2 = 7(Quotient)                     Reminder:0

2nd Division Iteration

Divide 7 by 2

     7 ÷ 2 = 3(Quotient)             Reminder=1

3rd Division Iteration

Divide 3 by 2

     3 ÷ 2 = 1(Quotient)              Reminder=1

Hence, the binary equivalent of the decimal number 14 is (110).

Step2:

Convert (13)₁₀ decimal number to binary number (?)₂ using division method

1st Division Iteration

Divide 13 by 2

     13 ÷ 2 = 6(Quotient)             Reminder=1

2nd Division Iteration

Divide 6 by 2

     6 ÷ 2 = 3(Quotient)             Reminder=0

6th Division Iteration

Divide 3 by 2

     3 ÷ 2 = 1(Quotient)             Reminder=1
  

Remainder from the last division iteration becomes MSD and reminder from 1st iteration becomes LSD.

Hence, the binary equivalent of the decimal number 13 is (101).

Step3:

Binary Division