355 Assignment 1 Fall 99
Due Wed 20 at 11:30 in class.

Question 1 (20 points):
(a) Prove x+xy=x using only Huntington's Postulates.
(b) Prove algebraically that (A(AB)')'=(AB')'

Question 2 (20 points):
(a) Use a K map to find a minimum SOP expression for  
G(a,b,c,d)= Pi M (1,4,9,12,13).
(b) Draw a circuit diagram that implements a  2 input exclusive or gate
using four  2 input nand gates. Only the true form of the variables are
available.

Hint: derive a SOP expression first, then convert to a nand-nand
realization (assume that variables are available in their true and 
complemented form). Then, use part (b) of Question 1 to
complete a 3 level nand only realization.

Question 3 (20 points):
Implement the function 
F(a,b,c,d,e)= Sigma m (8,9,10,11,12,13,14,15,16,18,20,22,25,27,29,31)
using a single 4-to-1 multiplexor. Assign variables a and b to the
control lines. You may assume that all variables are available in their 
true and complemented form.

Question 4 (20 points):
The majority function is specified as F(a,b,c)= Sigma m (3,5,6,7).  You
are given two components namely, and2op (a two input and gate) and
or3op (a three input or gate).  Given the following VHDL 
description, your task is to 
(a) develop entity and architecture descriptions for or3op
(b) complete the structural architecture for midStruct.

entity F is
   port
      (a,b,c : in bit;
       d     : out bit);
   end F;

architecture midStruct of F is

   component and2op
      port (x,y :in bit; z out : bit);
   end component;

   component or3op
      port (x,y,z :in bit; w out : bit);
   end component;

......

end midStruct;