HW2a - Boolean Algebra 1) Prove De Morgan's laws (for inputs A and B) by completing the truth table (fill in the appropriate column heading for the remaining columns): = (A+B) = AB (A.B)= A+B A B 0 0 B 0 1 0 1 1 1 2) Using Truth Tables prove: X e Y' EX OY (Remember is Exclusive OR and O is Exclusive NOR) X Y Y 0 0 0 1 1 0 1 1 3) Given truth table with 3 inputs X, Y, Z write the Boolean Expression for output F. (Hint: Start with the SOP or DNF and then use Boolean Algebra Laws to simplify.) F Y 0 Z 0 0 0 0 0 0 1 1 1 0 0 1 1 0 1 0 1 1 0 0 1 0 1 1 1 0 0 1 1 1 1 HW2b - Basic Building Blocks Combinational (Combinatorial) Logic Circuits 1) Multiplexor or Mux A 2-input Mux actually has 3 inputs A, B and the selector S and an output C as shown in the slides for Topic 1. If S=0 then the input A is selected and CEA and if S=1 then the input B is selected and C=B. The Truth Table for a MUX is shown. Write the Boolean equation for C (hint: write the SOP) and then draw the circuit using Logic Gates. Inputs Output ABS 0 0 0 C = 00 0 0 1 1 100 1 1 0 0 0 O 0 1 lolololo 1 0 1 1 0 1 1 1 1 1