ECE 102 - Homework 5

Due  09/29/2017

• 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. Given F′(A, B, C, D) = Σ m(0,1, 2, 3, 6, 7, 12, 13, 15).
   (a) Find the minterm expansion for F (both decimal and algebraic form)
   (b) Find the maxterm expansion for F (both decimal and algebraic form)
   
   
   
2. Given F(A,B,C,D) = (A+B'+D)(A+B+D')+C and
         G(A,B,C,D) = BC'D' + B'C'D'+ (A+BC)(A'D+AC')
   Use algebraic techniques (do not use truth table) to express F, F', G and G'
    a) as  minterm expansions using m/M notation
    b) as a maxterm expansions using m/M notation
   
    c) Write the minterm expansion for F'+G using m/M notation
    d) Write the maxterm expansion for F'+G using m/M notation
    e) Write the canonical SOP of F'+G using algebraic notation
   
   
    f) Write the maxterm expansion of FG' using m/M notation 
    g) Write the minterm expansion of FG' using m/M notation
    h) Write the canonical POS expansion of FG' in algebraic notation
   
   
   
3. Design a four input (A3,A2,A1,A0)  single output (Z) circuit as follows.
   The output of the circuit   is 1 if and only if the 4 bit binary number applied to the input is not divisible by 2 or 3.   Use the minimum number of logic gates possible.