Using Boolean Algebra, simplify the following expressions: a. F(x, y, z) = xy + x + XZ + XX +XX7 b. Implement the simplified expression of F in part (a) using 4:1 mux. Hint: construct a truth table Parts c & d:Using K-map below for F(A,B,C,D): Use each map separately. c. give the simplified minimal SOP d. give the simplified minimal POS 01 11 AB CD 00 01 11 10 SOP = 00 1 0 0 0 0 0 0 d d 1 10 1 1 1 1 AB CD Gate NOT POS= 00 01 11 10. 00 01 2-input NAND 3-input NAND 2-inpur NOR 3-input NOR 2-input AND 3-input AND 2-input OR 3-input OR 2-input XOR 1 d 0 Ipd (ps) 15 20 0 0 30 30 45 30 40 40 5.5 60 0 11 O e. For the simplified POS, implement the function using NAND and INV gates only. | f. Use the delay information in the table, give the longest path and shortest path for the circuit in part e. P d 10 tcd (ps) 10 15 25 25 35 25 30 30 45 40 1 1 1 1