Convert the following base 10 (decimal) numbers to base 2(binary):
107
200

107₁₀ - 1101011

₂ (Binary representation)

200₁₀- 11001000₂ (Binary representation)

Explanation:

Converting from Decimal to binary:

Procedure -

1. Divide the number by 2, write the reminder separately.

2. Divide the divisor by 2, write the reminder before the previously written reminders.

Keep doing this till you get your divisor as 1.

Then we will write the divisor  before the written reminders and that will be the binary representation.

 For 107 :

          We divide 107 by 2 ,we get the divisor 53 and remainder 1

                                                  ( 1 )

Then,we will divide this divisor i.e 53 by 2,we get divisor 26 and remainder 1 ,we will put this remainder before the previous one.

                                                ( 1 1 )      

Then,we will divide this divisor i.e 26 by 2,we get divisor 13 and remainder 0 ,we will put this remainder before the previous one.    

                                                 ( 0 1 1 )

Then,we will divide this divisor i.e 13 by 2,we get divisor 6 and remainder 1 ,we will put this remainder before the previous one.    

                                                 ( 1 0 1 1 )

Then,we will divide this divisor i.e 6 by 2,we get divisor 3 and remainder 0,we will put this remainder before the previous one.    

                                                 ( 0 1 0 1 1 )

Then,we will divide this divisor i.e 3 by 2,we get divisor 1 and remainder 1  ,we will put this remainder before the previous one.    

                                                 ( 1 0 1 0 1 1 )

As we get the divisor=1,then we will stop.we will write the divisor before the written reminders.

                                              ( 1 1 0 1 0 1 1 )

This will be the binary representation of 107.

For 200 :

         We divide 200 by 2 ,we get the divisor 100 and remainder 0

                                                  ( 0 )

Then,we will divide this divisor i.e 100 by 2,we get divisor 50 and remainder 0 ,we will put this remainder before the previous one.

                                                ( 0 0 )      

Then,we will divide this divisor i.e 50 by 2,we get divisor 25 and remainder 0 ,we will put this remainder before the previous one.    

                                                 ( 0 0 0 )

Then,we will divide this divisor i.e 25 by 2,we get divisor 12 and remainder 1 ,we will put this remainder before the previous one.    

                                                 ( 1 0 0 0 )

Then,we will divide this divisor i.e 12 by 2,we get divisor 6 and remainder 0 ,we will put this remainder before the previous one.    

                                                 ( 0 1 0 0 0 )

Then,we will divide this divisor i.e 6 by 2,we get divisor 3 and remainder 0  ,we will put this remainder before the previous one.    

                                                 ( 0 0 1 0 0 0 )

Then,we will divide this divisor i.e 3 by 2,we get divisor 1 and remainder 1,we will put this remainder before the previous one.    

                                                 ( 1 0 0 1 0 0 0 )

As we get the divisor=1,then we will stop.we will write the divisor before the written reminders.

                                                 ( 1 1 0 0 1 0 0 0 )

This will be the binary representation of 200.