## CSE370 Assignment 2

### Distributed: 2 April 1999 Due: 9 April 1999

1. Katz, Chapter 2 (pp. 40-85 and 92-102).

#### Exercises:

1. Katz exercise 2.3 without using inverters (only 2-input NAND gates).  Draw the schematic in DesignWorks and verify its operation by exercising all input combinations using a set of three switches. Turn in the schematic drawing.
2. Katz exercise 2.7 (a,b,c,d).
3. Prove the consensus theorem (xy+yz+x'z = xy+x'z) by two methods:

4. (a) using a truth table and
(b) using the laws of Boolean algebra.
5. Katz exercise 2.10 (b, g).
6. Katz exercise 2.12 (do the verification in DesignWorks using switches).  Turn in the schematic drawing.
7. Give a Boolean function that cannot be realized using:
(a) only AND and OR gates;
(b) only XOR gates.
8. Find and simplify the complement of the following functions:
(a) F = x'y'z + x'yz + xyz
(b) G = yz + x(yz' + z)
Turn in DesignWorks schematics for both the functions above and their minimized complements.
9. Consider the function f(A, B, C, D) = Sm(0, 1, 2, 5, 6, 8, 10, 14).
(a) Write this as a Boolean expression in canonical minterm form.
(b) Rewrite the expression in canonical maxterm form.
(c) Write the complement of f in "little m" notation and as a canonical minterm expression.
(d) Write the complement of f in "big M" notation and as a canonical maxterm expression.
10. Consider the function f(W, X, Y, Z) = YZ' + W'Y'Z + X'Z'.
(a) Express the function in canonical sum-of-products form.  Use "little m" notation.
(b) Express the complement of the function in canonical product-of-sums form.  Use "big M" notation.

#### Rationale:

• To practice and gain facility with Boolean algebra and canonical forms.
• To start using a logic schematic diagram editor and simulator.

Comments to: cse370-webmaster@cs.washington.edu (Last Update: 04/02/99)