Digital Circuits

  1. Draw a logic circuit (using AND, OR, and NOT gates) that implements the following expression.  Do not attempt to minimize the expression.


  2. Find a disjunctive normal form expression that represents the function given in the following truth table:


    3.             _     _     _ _
    x y z + x y z + x y z + x y z
     
  3. Minimize the following DNF using Boolean algebra:


    4.           _     _   _     _ _       _
    x y z + x y z + x y z + x y z + x y z
              _      _     _      _     _
    = x z(y + y) + y z(x + x) + x z(y + y)
              _     _
    = x z + y z + x z
            _      _
    = x(z + z) + y z
            _
    = x + y z
     
  4. Minimize the following DNF using a Karnaugh map.

    5. minimized expression:  x + y