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HOMEWORK-1 (Note: HW submission will be accepted via blackboard only; you can scan and upload a pdf of your final work via the HW-page on blackboard. Note: For class homework and unlike lab exercises, you can use multi-input gates and not be limited to 2 input gates only) Q1: Find simplified SOP (Sum of Product) expression (and circuit) for the following function (Note: mention the Boolean property number that you apply to simplify the Boolean expressions. Also unlike lab exercises, you can use multi-input gates and not be limited to 2 input gates only) F(x1,x2,x3)=m(1,3,4,6,7) Q2: Find simplified POS (Product of Sum) expression (and circuit) for the following output function (Note: mention the Boolean property number that you apply to simplify the Boolean expressions) F(x1,2,x3)=(3,4,6,7) Q3: Find simplified POS (Product of Sum) expression (and circuit) for the following output function (Note: mention the Boolean property number that you apply to simplify the Boolean expressions) F(x1,x2,x3)=M(0,2,5) Q4: Prove that m(1,2,3,4,5,6,7)=x1+x2+x3 (Hint: start from the Left Hand Side LHS and write the expressions for the min terms and then simplify using the Boolean properties as discussed in the class. Also mention the Boolean property number that you apply to simplify Boolean expressions.) Q5: Design simplest (lowest-cost) circuit of four variables (x1,2,3,4) which produces an output value of f=1 when two or more input variables have the value of ' 0 ; ; otherwise f=0; Calculate cost of your final lowest-cost circuit that you design. (Hint: start with the truth table of four variables, write all combinations for the input variables, and if you have 2 or more ' O 's than ' 1 's in a given row then output f=1 otherwise f=0; Try both the SOP form and POS form of the output function to compare and find the lowest-cost circuit. For homework and unlike lab exercises, you can use multi-input gates and not be limited to 2 input gates only.)