CS100 - Assignment 3 (Architecture)

(Section 001, Fall 2007)

The questions carry equal weight. Please show the computations leading to the result. Show all your work for full credit!

1. Fill in the missing parts of the following truth table and show that (NOT (P or Q)) has the same values as (NOT P) AND (NOT Q)

   
   

   P	Q	(P OR Q)	NOT (P OR Q)	NOT P	NOT(Q)	(NOT P) AND (NOT Q)
   0	0
   0	1
   1	0
   1	1

2. Construct a circuit using two-input ANDs, ORs, and one-input NOT gates that is equivalent to a three-input AND gate that has the output 1 if and only if all three inputs are 1.

3. Build and fill in the truth table that describes the action of the following circuit, and give the equivalent Boolean expression for the output.

4. Write the truth table for (NOT (A AND B)) and for ((NOT A) OR (NOT B)). Show that the two are equivalent.

5. Let A and B be Boolean inputs. Find the Boolean expression that will produce S and C in the following truth table and draw the corresponding circuit diagram.

   
   

   A	B	C	S
   0	0	0	0
   0	1	0	1
   1	0	0	1
   1	1	1	0