Construct a truth table then simplify the following functional expressions: a) F(x,y,z) = xyz + x(yz)' + x'(y+z) + (xyz)' b) F(x,y,z) = y(x'z + xz') + x(yz + yz') 2. Simplify the following functional expressions using Kmaps or Boolean algebra and its identities. List the identity used at each step. b) y'(x'z' + xz) + z (x + y)' Little John is trying to train his new puppy. He is trying to figure out when the puppy should get a dog biscuit as a reward. He has concluded the following: 1) Give the puppy a biscuit if it sits and wiggles but does not bark. 2) Give the puppy a biscuit if it wiggles but does not sit or bark. 3) Give the puppy a biscuit if it wiggles and barks. 4) Don't give the puppy a treat otherwise. Use the following: S: Sit (0 for not sitting; 1 for sitting) W: Wiggles (0 for not wiggling; 1 for wiggling) B: Barking (0 for not barking; 1 for barking) F: Biscuit function (0, don't give the puppy a biscuit; 1, give the puppy a biscuit) Construct a truth table and find the minimized Boolean function to implement the logic telling John when to give his dog a biscuit.

If F(w,x,y,z) = w'x'y'z' + w'z + w'x'yz' + w'xy'z' + wx'y a) Create the Kmaps and then simplify F(w,x,y,z) (leave in sum-of-products form). b) After simplifying F(w,x,y,z) draw the combinational circuit that directly implements the Boolean expression.