Simplify the following functions using a K-map and obtain the minimal SOP and POS implementations for each function (4 expressions total). a) F(A, B, C, D) = sigma m(0, 2, 3, 5, 7, 8, 9, 10, 13, 15) b) G(A, B, C, D) = Product M(0, 1, 4, 8, 9, 10, 12, 14) Given the following K-maps, obtain the SOP and POS expressions for each and simplify them to obtain the minimal implementations. Write both the original long form (i.e. where each term is a minterm or maxterm) and the simplified form you obtain from the K-map. Do not write the compressed form using indices for either expression. A) CD b) Implement the following functions using only a) NAND gates and b) NOR gates (i.e. 2 different implementations for each function). Simplify each circuit if any simplifications are possible. You can use a K-map to make each equation clearer and simplified. a) F(A, B, C) = (A + B)BC b) G(A, B, C, D) = D+ AB(BC) Find the minimal NAND-NAND and NOR-NOR expressions for the following functions (4 total): a) F(A, B, C, D) = sigma m(0, 2, 5, 9, 11, 15) + dc(1, 3, 4, 12) b) G(A, B, C, D) = Product M(0, 1, 3, 8, 9, 15) Find the critical path and the fastest for the circuit below and indicate their delays. The delays are as follows: NOT = 1ns, AND = 3ns, OR = 3ns, NAND = 2ns, NOR = 2ns, XOR = 4ns