CSC270 Midterm Prep 2012

--D. Thiebaut 08:40, 9 March 2012 (EST)

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Below are some problems that will help you prepare for the midterm.

• Assume you have a boolean function f defined as:

f = Σ(1,3,5).

Give the maxterm canonical form of f.

• Implement f above with NANDs only. With NORs only.

• Assume that you have a desk with 3 drawers and a secret compartment. The drawers have electronic sensors that detect if a drawer is open (1) or closed (0). We want to build a simple circuit that will activate a release signal (set it to 1) to open the secret compartment only if the right combination of steps is taken.

This combination of steps is:

1. All drawers are closed
2. Drawer 1 is open
3. Drawer 1 is closed
4. Drawer 3 is open and stays open
5. Drawer 2 is open
6. Drawer 2 is closed

At this point the release signal is activated. It stays on as long as none of the drawers move. The secret compartment opens!

Question

How many states does this FSM have?

• Implement the function below with a 4-to-16 decoder. The decoder has active-low outputs and an active-low enable. Be efficient in your design.

f = Σ(0,1,3,4,5,6,7,8,9,10,11,12,14)

• Implement a 3-to-8 decoder with several 2-to-4 decoders. You may assume that the decoders have

enable inputs, and you are free to choose active-high or active-low signals.

• What is the boolean representation of the function f shown in the figure below? Express f in its

simplest form.

• What is the state diagram of the sequential circuit shown below, if D2 is set to 1 always? If D2 is set to

0 always?