Computer Lab supervisions - Digital Electronics

This is usually a fun course. As you can expect, it's very logic but it does have tricky parts (e.g. designing state machines and dealing with MOS transistors). The Harris & Harris book is quite good for the digital part.

A 5th supervision is sometimes requested by students but not needed by default.

**Supervision 1:**

- Exercises 1-5 from the Example Sheet.
- The conjunctive normal form for a boolean function
*F*on three variables consists of a product of sums, with each sum containing three literals. How would you use the truth table of*F*to obtain an expression for*F*in this form? - Design a vending machine control circuit. A soft drink costs 45c, and your circuit records the nickels (5c), dimes (10c), and quarters (25c) fed to the machine. It issues a command to dispense a can when the appropriate payment has been equalled or exceeded. Assume that at least one quarter is used and that coin counters make available binary counts for each kind of coin.
- How would a five-variable Karnaugh map look like? (remember the adjacency property of Karnaugh maps given by the Gray code). How would you expand to six or seven variables and beyond?
- How many (different) possible functions can be mapped on a two, three and four-variable Karnaugh map? For each case, what is the proportion of possible functions that cannot be simplified?

**Supervision 2:**

- Solve the vending machine question from last supervision without any assumption, i.e. any number of quarters is now possible, including zero.
- Questions 6-13 from the Example Sheet.
- CST 1995 Paper 2 Question 21 (it's an incomplete Karnaugh map, X means not yet determined so can be 0 or 1 which is up to you to replace accordingly).
- CST 2002 Paper 2 Question 2.
- Determine and prove whether applying DeMorgan can change (i.e.
add or remove) static hazards of a logic circuit.
*Hint*: using only boolean algebra may not get you very far.

**Supervision 3:**

- Questions 14-18 from the Example Sheet.
- CST 2001 Paper 2 Question 3.
- CST 2002 Paper 2 Question 3.
- CST 2003 Paper 10 Question 1.
- Design the vending machine from last supervision using sequential logic, i.e. build a proper finite state machine. Assume no initial coins exist in the machine. Draw the state diagram and state table as well as the minimized form of the algebraic expressions for the next states. You are free to choose the flip-flop type.

**Supervision 4:**

- Questions 19-22 from the Example Sheet.
- CST 2000 Paper 2 Question 3.
- CST 2000 Paper 10 Question 9.
- CST 2001 Paper 10 Question 1.
- CST 2004 Paper 2 Question 2.