Minimize the following Boolean functions using K-maps: a) f (a, b, c) b) f (a, b, c, d) = c) f (a, b, c) = d) f (a, b, c, d) = e) f (a, b, c, d) = (2, 3, 6, 7) (2, 3, 6, 7, 12, 13, 14) (0, 3, 4, 7) (1, 3, 4, 5, 6, 7, 9, 11, 13, 15) (0, 2, 4, 5, 6, 7, 8, 10, 13, 15) Question 9: A logic circuit has four inputs a, b, c and d and one output z. The output is 1 if and only if the number of 1's in b and c is greater than or equal to the number of 1's in a and d. For example, if abcd = 0001, then z = 0; if abcd = 1110, then z = 1; if abcd=0000, then z = 1, and so on Write the truth table for z Minimize the expression for z Implement the circuit using a 2-level NAND-NAND logic