Number Base Conversion Practice

This is a paper and pencil exercise.

1. Complete the table. Show your calculation. Each column represents a base and each row should have the same number in it, represented by the various bases.


2. Fill in the blanks. Each question mark stands for a single digit.

0x?4 = 124?5

3. How can you use % to obtain the last digit of a number represented by the symbol x? The last two digits? What can you say in general?

4. A Balanced Ternary Expansion It is possible to uniquely write any integer in an expansion of the form

$$e_0 + 3e_1 + 3^2e_2 + \cdots + 3^ne_n, $$

where each of the \(e_k\) are 0, 1 or -1. Find such an expansion for each of the folllowing numbers: 5, 13, 37 and 79. Can you describe an algorithm for doing this in general?

5. Be an agent of Change Describe how to count out any amount between $0.00 and $1.00 using standard coins to use as few coins as possible. You will find using // and % handy. NB: Gordon Gecko is your friend.