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CSE370 Assignment 3

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Distributed: 9 April 1999

Due: 16 April 1999

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Reading:

Katz, Chapter 3 (pp. 110-122).

#### Exercises:

- Reverse engineer the circuit shown in the schematic below in order to
minimize it into a more efficient implementation.

(a) Find the Boolean expression that describes the circuit.

(b) Construct the truth table for the function.

(c) Write the function in canonical sum-of-products form (little m notation).

(d) Simplify the function above using the axioms/theorems of Boolean algebra
(show each step).

(e) Simplify the function again using a Karnaugh map. Give the Boolean
equation that results from your simplification.

(f) Suppose your system specification suddenly changed (as frequently
happens in the real world) and you now need a circuit that implements the
complement of F. Show how you can use another instance of the K-map for F
to find the minimized form of the complement F'. Give the minimized
Boolean equation for F'.

(g) Draw the minimized F from part (e) and F' from part (f) in DesignWorks and
verify thier operation with binary switches and probes. Turn in your
schematics. Make sure to verify your circuit using DesignWorks's simulator.
- Katz exercise 2.19 (a).
- Katz exercise 2.20 (c, d).
- Katz exercise 2.24.
- Katz exercise 2.27.
- Katz exericse 2.29 (but, do it for an EVEN number of 1s).
- Katz exercise 3.2 (c) (turn in a DesignWorks schematic).
- Katz exercise 3.3 (c) (turn in a DesignWorks schematic).

#### Rationale:

- To practice and gain facility with two-level logic minimization.
- To understand the benefits of using don't care information in minimization.
- To practice basic combinational logic design.

Comments to: cse370-webmaster@cs.washington.edu
(Last Update: 04/12/99)