ECE 102 - Homework 3

Due  09/14/2017

    Follow the guidelines for preparing homework solutions.
    Graded homework will be distributed during labs. Provide your name and the lab section number on top of the first page.
    Turn in solutions to all the problems.  Only a subset of  problems will be graded. Points will be taken off for problems not submitted.

1. 1. Use DeMorgan's Law to find the complement of
   F = (A + (B'CD')'+E')(A'B +C'D+E)
   G = (A'+B+C)'(B+C'D')+ B'C'
   H = B(AC'+A'C)+B'(AC+A'C')
   Do not simplify.
   Check your answer using a truth table for F and F'.
   
   
2. Write the dual of the following expressions or equations:
   a) F = (A+BC+D')+(A'B'+CD).(CD'+A'C')
   b)(X + Y')Y = XY
   c)(X + Y)(Y + Z)(X' + Z) = (X + Y)(X' + Z)
   d) A + BCD = (A + B)(A + C)(A + D)
   
   
3. Simplify the following expressions to a minimum sum of products. Only individual variables should be complemented.
   a)  [ (XY)' + (X'+Y')'Z]
   b)  (A + (B(C'+D')')')'
   c)  [(P'+Q)' + (PQ'R)' +R'S]'
   d)  [AB' +(C+D)' +E'F](C'+D)
   e)  (A+B)'C'D' + (A+BC)'
   
   
4. Draw a circuit to realize the function
      F= AB'C' + A'B'C'  + AB'C + ABC'
   a) Using one OR and three AND gates. The AND should have two inputs
   b) Using two OR and two AND  one AND and three OR  gates.  All of the gates should have two inputs.
   
   
5. Multiply to obtain a sum of products. Simplify the answer.
   a) (A'+B'+D)(A'+B)(B'+C+D')(A'+B+C)(B+D)
   b) (A'+B'+C')(B+C+D')(A+B)(B'+D)(B'+C+D)
   c) (B'+C+D')(A'+B+D')(B+D)(A'+C+D)(A'+D)
   d) (A+B+C)(A+C+D)(A'+B'+C')(A'+C'+D')
   
   
6. Factor to obtain a product of sums:
   a) A'B'C+AC'D+ABC+BC'D'      (four terms)
   b) P'Q'+PQ+Q'R'S + QRS       (four terms)
   c) AB+A'B'C+ B'C'D+ BC'D'    (four terms)
   d) A'C'D+AB'D'+A'CD'+BD      (four terms)
   e) WXY + WX'Y+WYZ +XYZ'      (three terms) 
   
   
7. Simplify each of the following expressions:
   a) xy' + z + (x'+y)z'
   b) A'B'CD + A'B'C'D + BEF + CDE'G + A'DEF + A'BEF ( reduce to sum of three terms)
   c) [(a'+d'+b'c)(b+d+ac')]' + b'c'd' + a'c'd   (reduce to three terms)
   
   
8. Given f(X,Y,Z)= Z'(XY+X'Y'),
   a) Express f as a minterm expansion
   b) Express f' as a minterm expansion
   c) Express f as a max term expansion
   d) Express f' as a max term expansion.
   Use m/M notation.