CSI 250 - HW2

~A means not A in an expression. ~AB would this mean (not A) and
B. This is different than ~(AB) which would mean not (A and B).


1. Use a Karnaugh map to simplify:
  A ~B ~C + ~ABC + AB ~C + ~A ~B ~C

2. Use a K-map to find a simple expression for f(A,B,C,D). f is 1 when
   two or more inputs are 1. f is 0 otherwise.

3. Use a K-map to find a simple expression for f(A,B,C,D). f is 1 when
   precisely two inputs are 1. When three or four inputs are 1, then
   the result does not matter. The function f is 0 otherwise.

4. A logic circuit has three inputs a,b, and c. abc represents 3 bits
   to form a number from 0 to 7. The outputs of the circuit are
   u,v,w,x,y, and z. uvwxyz represents the square of the input. So if
   abc is 7, then uvwxyz will be 49. Write 6 truth tables for uvwxyz
   and then simplify the terms using a Karnaugh map.

5. Briefly describe the utility of a PLA. 

6. If the clocks refresh rate is 2 gigahertz (use 2,000,000,000 Hz),
   then what is the cycle time of the clock in seconds? How about in
   nanoseconds?