d) With NAND gates e) With NOR gates Question 7: Minimize the following Boolean functions using the algebraic method. f1=x, yz + xz t2=(x+y),(x, + y') a) d) f4 (a, b,c, d) 2(0-3,5,7,8-11, 13, 15) Question 8: Minimize the following Boolean functions using K-maps a) f (a, b, c)= (2, 3, 6, 7) b) f (a,b,c,d)= (2, 3, 6, 7, 12, 13, 14) c) f (a, b, c)= (0, 3, 4, 7) d) f(a,b,c,d)= (1, 3, 4, 5, 6, 7, 9, 11, 13, 15) f (a,b,c,d)= (0, 2, 4, 5, 6, 7, 8, 10, 13, 15) e) 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-11 10, then z = 1; if abcd = 0000, then z 1, and so on Write the truth table forz Minimize the expression for z Implement the circuit using a 2-level NAND-NAND logic