Use Logisim to answer the following questions:

Questions 1. Draw the truth table and logic circuit for the following Boolean function: F(A)=AA What function is this circuit performing? If you had to design a logic circuit using only NAND technology, how would the above circuit prove useful? 2. Prove the following equations are true using the laws and properties of Boolean algebra: a) X(X+Y)=X b) X(X+Y)=XY c) (X+Y)(X+Y)=X For each equation, explain how Boolean algebra is useful for reducing the number of gates in a logic circuit (i.e. explain how many gates are used on each side of each equation). 3. For the 2-bit multiplier designed in class, simplify the equation for Z1 using Boolean algebra to show that: Z1=X1X0Y1Y0+X1X0Y1Y0+X1X0Y1Y0+X1X0Y1Y0+X1X0Y1Y0+X1X0Y1Y0=X1X0Y1+X0Y1Y0+X1X0Y0+X1Y1Y0 4. Using Logisim, create the 2-bit multiplier designed in class using the minimized Boolean equations