CSE370 Assignment 2

Distributed: 2 October 2000
Due: 9 October 2000

Reading:

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

Exercises:

1. Draw a schematic in DesignWorks for the following function: f(A,B,C,D) = (AB' + C'D)'
   (a) using only two-input NOR gates, and
   (b) using only two-input NAND gates.
   Verify the operation of each circuit by exercising all input combinations using a set of four switches at the inputs and a probe at the outputs. Turn in a schematic drawing for each circuit showing the inputs combination A=0, B=1, C=0, D=1.
2. Prove the following using the truth-table method.
   (a) (A + B')B = AB
   (b) (A + B)(A' + C) = AC + A'B
   
3. Prove the following theorems of Boolean algebra using other theorems and laws (list the number of the law you use for each step) after first "multiplying out" the expressions.
   (a) (A + B)(A + C) = A + BC
   (b) AB + A'C = (A + C)(A' + B)
4. Use DeMorgan's theorem to compute the complement of the following Boolean expressions.
   (a) ABC + B(C' + D')
   (b) A + (BC)'
5. Demonstrate that a two-input NOR gate is a universal logic element. You can do this by showing how they can be used to make: NOT, AND, OR, and XOR gates. Remember that each input of the NOR gates must be used, it can not be left unconnected. Is an XOR gate a universal logic element? Why or why not? What about a two-input NAND gate?
6. Consider the function f(A,B,C,D) = Sm(1, 2, 3, 5, 8, 13).
   (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.
7. Consider the function f(A,B,C) = AB + B'C' + AC'
   (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.