Name __________________________                                                              Date: ___/___/____

Mr. Merlis                                                                                                                   Block ___3 - _____

AP CS - Java                                                                                                            Day of Class: _34_

Converting Between Bases

 

We use a “base 10 positional notation” system. 

In simple terms, it means that each digit in a number corresponds to the number of multiples of the base at that power.

 

Ie. 37910­ = 3 x 102 + 7 x 101 + 9 x 100

 

To convert from base10 to base8, we must first think how the number should appear:

 

            __ x 82 + __ x 81 + __ x 80

 

In the case of 379,  82 (64) goes into it 5 times (with a remainder), so we immediately have:

 

            5 x 82 (320)

            _ x 81

            _ x 80

 

Having already the value of 320, only 379-320 = 59 remains.

 

So now we divide 59 by 8 (81) and we get 7 (with a remainder), giving us:

 

5 x 82 (320)

            7 x 81 (56)

            _ x 80

 

Only needing 59 more and getting 56 leaves us with a remainder of 3.  Since we are now at the units digit, we can simply put it there, giving us a final answer of:

 

 

5 x 82      +        7 x 81       +       3 x 80

 

 

Convert the following two base10 numbers into the given base.

 

 

                                    a) base 8                                  b) base 16                                 c) base 2

 

 

 

 

  1. 2510      

 

 

 

 

 

 

 

 

  1. 7910