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.

281016
10111100
0125
224
0xFF5

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.