Homework 2 Examples

Purposes:
   (1) work with combinational logic;
   (2) work with sequential logic.


1. Consider A*( (~A) + B ) = A*B.  Show by truth table that this is true.

     A B | ~A | ~A + B | A*(~A+B) | A*B
    -----+----+--------+----------+-----
     0 0 |  1 |    1   |    0     |  0
     0 1 |  1 |    1   |    0     |  0
     1 0 |  0 |    0   |    0     |  0
     1 1 |  0 |    1   |    1     |  1     true because the table is an
                            ^        ^     exhaustive enumeration and the
                             \______/      last two columns are the same


   Show by algebraic manipulation that this is true.

       A*( (~A) + B )
     = A*(~A) + A*B    by distributive postulate
     =   0    + A*B    by inverse postulate
     = A*B             by identity postulate


2. Determine the simplest logic expression for the values in this Kmap:

  \BC
  A\  00   01   11   10
    +----+----+----+----+                    _ _ _   _ _       _ _       _
  0 |  1 |  1 |  0 |  0 |  sum of products = A*B*C + A*B*C + A*B*C + A*B*C
    +----+----+----+----+                      _
  1 |  1 |  d |  d |  1 |      don't cares = A*B*C + A*B*C
    +----+----+----+----+
                              _
  simplified expression = A + B   (treat both don't cares as true)


3. [see pdf file for examples of sequential logic questions]