Question

Convert the following fractions to binary. If you encounter a repeating pattern, include only the first occurrence in your responce

0.75

0.625

0.35

Answer 1

when dealing with converting a decimal number having fractional part we need to multiply the fractional part by 2 and take the decimal part as a remainder. In next step, the fractional part of previous result will be taken for multiplication with 2. This process will continue untill the fractional part become 0 or else if the same fraction pattern is repeating or becoming unended. Then we read from top-to-bottom for the binary equivalent.

we have the numbers 1) 0.75     2) 0.625      3) 0.35

here the decimal part(not after fraction) is 0 in every case so its binary will be 0 only.

we can convert the fraction part of these numbers as follows:

1) 0.75

                                          carry(binary)

         0.75 * 2 = 1.5                    1

         0.5   * 2 = 1.0                    1    (considering only numbers after fraction)

here the fraction has become 0, so we can stop here.

therefore (0.75) = (0.11)₂ in binary (reading from top to bottom in carry cell)

2) 0.625

                                             carry(binary)   

         0.625 * 2 = 1.25                     1

         0.25 * 2   = 0.5                       0

         0.5 * 2    = 1.0                       1

here also the fraction has become 0, so we can stop here.

therefore (0.625) = (0.101)₂ in binary.

3) 0.35

                                              carry(binary)

        0.35 * 2 = 0.7                          0

        0.7 * 2 = 1.4                           1

        0.4 * 2 = 0.8                            0

        0.8 * 2 = 1.6                            1

        0.6 * 2 = 1.2                             1

        0.2 * 2 = 0.4                             0  

        0.4 * 2 = 0.8                             0

here we can see same fraction is repeating from this step(same as step 3). So the result will be replicated without ending.

therefore (0.35) = (010110)₂ in binary (Since : In your question they are mentioning " If you encounter a repeating pattern, include only the first occurrence in your responce")