Analyze the cellular array

Question

Solve the following problem:

Analyze the cellular array in the Fig. A consisting of four different types of cells A, B, C, and D, and determine the output functions f and g. Fig. B shows a cell with two control inputs z1 and z0 to determine the contents of the cell which can replace any of these cells in this array

(z₁,z₀) = (0,0) → A,
(z₁,z₀) = (0,1) → B,
(z₁,z₀) = (1,0) → C,
(z₁,z₀) = (1,1) → D.

               Figure (A)   Array                                                                  Figure (B) : Module in the array