For a Boolean function of n variables, we can index a min-term (c.g., X XX3X) by m, (i = 0, 1,..., 2"-1) and we can determine the index i as follows: we construct a binary number of n bits by putting a 1 corresponding to the positions of a direct term and a 0 corresponding to a complemented term (XXX3X (1000)2) then we convert this binary number to the decimal number i=8 ((1000)28). Consider the following function: F = f(A, B, C, D)= mo + m + m + ma + ms+ms + M15 (1) a) Construct the truth table. (4 points) b) Write the function in SOP and POS form. (5 points) c) Using K-Map to simplify the function and write the simplified function. (6 points) d) Draw the circuit according to the function you wrote in c) only use AND, OR, NOT gates. (5 points) e) Consider the function: G = g(A, B, C, D) = A + AB+ AD+B+BD+BCD (2) Simplify the function (using logic properties or the K-map) to the most simplified form and draw the circuit with only NAND gates. (10 points) Hint: DeMorgan's Theorem XY=X+Y.