Ignore the HDL part in the following problems 4.31 and 4.32. 4.31 Construct a 16 x 1 multiplexer with two 8 X 1 and one 2 × 1 multiplexers. Use block dia- grams. (HDL-see Problem 4.67.) 4.32 Implement the following Boolean function with a multiplexer (HDL-see Problem 4.46): (a) F(A, B, C, D) = (0,2,5, 8, 10, 14) (b) F(A, B, C, D) = II(2, 6, 11) 4.34 An 8 x 1 multiplexer has inputs A, B, and C connected to the selection inputs S2, S₁, and So, respectively. The data inputs I, through I, are as follows: (a) = = = 0; 1= Is= 1; 1= 14= D; and I= D'. (b) == 0; 13-17=1; 14 = Is =D; and Io = 16 = D'. Determine the Boolean function that the multiplexer implements. 4.35 Implement the following Boolean function with a 4 x 1 multiplexer and external gates. (1, 3, 4, 11, 12, 13, 14, 15) (a) F₁(A, B, C, D) = (b) F₂(A, B, C, D) = == (1, 2, 5, 7, 8, 10, 11, 13, 15)