CSC270 Midterm Prep 2012

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

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Below are typical questions you can expect on 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.

• 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?

• 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!

• We want to implement a GYR sequencer where Green stays on for approximately 1 minute, Yellow for approximately 15 seconds, and Red for approximately 45 seconds. You have available to you a clock generator that generates a 1Hz, 1KHz, and 100KHz signal.
  • Figure out a way to generate a simple design with as few states as possible.
  • How many flip-flops will you need?