Assignment 3 (Assigned August 27)

1. Suppose you want to represent the following positive integers in trinary. Indicate how many trinary digits are required to represent each of the following sets of integers:

(1) The integers from 0 to 127 inclusive
(2) The integers from 0 to 2,048 inclusive
(3) The integers from 0 to 32,500 inclusive
(4) The integers from 0 to 1,500,345 inclusive

2. Indicate how many trinary digits (trits) are needed to represent (1) 4-bit, (2) 12-bit, and (3) 24-bit binary numbers.

3. Convert each of the following binary numbers into hexadecimal form. Assume these quantities represent unsigned integers.

(1) 1010;  (2) 10010; (3) 0111110; (4) 10000000; (5) 0111111

4. Convert each of the following decimal numbers into hexadecimal.

(1) 111; (2) 147; (3) 511; (4) 8100; (5) 8511

5. Suppose you are a jogger who wants to use your ten fingers to count laps as you circle a track. How many laps can you conveniently count? Briefly justify your answer.