Current Topics in HCI - Winter Semester 2004/2005
Due on Thursday, December 16, 2004 during class
In the last lecture, we talked about how to use matrices to represent state transitions. In this assignment, you will work through a simple example.
Let's say we have a TV with three channels, 1 to 3 (we will use only three channels for simplicity). The TV's remote has two buttons (CH_UP and CH_DOWN) for cycling through the channels in both directions. It also has 3 buttons for jumping to a specific channel directly.
- Draw a state diagram of the TV's channels, labelling all of the interconnections appropriately.
- Recall that state transitions can be represented by the matrix formula s' = sB. What is s for each of the three channels?
- Write the matrix B for each of the five buttons (CH_UP, CH_DOWN, 0, 1, 2).
- Show, using matrix algebra, that CH_UP is the "undo" for CH_DOWN and vice versa.
- Is it possible to "undo" the state transition from pressing the 0, 1 and 2 buttons? Write the matrices or prove that they do not exist.
Extra Credit: Suppose now your TV has 99 channels. In addition to the CH_UP and CH_DOWN buttons, you have a numerical keypad with keys 0 to 9 for jumping to any channel. Channels are always input as two digit numbers (i.e. 01, 02, ... 99). What do the matrices for CH_UP, CH_DOWN and the 10 keys on the numerical keypad look like now? Is there a way to reduce the size of these matrices using a matrix transform?
You may work on this assignment by yourself or in groups of 2. It may be helpful to refer to the reading.
Hand in your submission before the end of the lecture on Thursday, December 16.
If you wish to submit your assignment electronically, email a PDF to
The assignment will be graded on the following rough scale:
- 1.0 - exceptional work that clearly went above and beyond what was expected from the exercise
- 2.0 - exercise was completed satisfactorily as per the assignment specification
- 3.0 - exercise was completed, but has some problems
- 4.0 - incomplete exercise
- 5.0 - little or no effort was put into the exercise
Late assignments will be graded with a penalty of 0.5 per 24 hour period after the due date.