2 Create K-maps and then simplify for the following functions: (20 pts) 1) F(x,y,z)=xyz+xyz+xyz 2) F(x,y,z)=yz+xy+z 3) F(x,y,z)=xyz+xyz+xyz+xyz 4) F(x,y,z)=xy+yz+xz 5) F(x,y,z)=xy+yz+x+y+xyz 3 Simplify the following Boolean functions using Boolean algebra and its identities. List identities used at each step. (20 pts) 1) F(x,y)=xy+y+xy 2) F(x,y,z)=xyyz+x+y+z 3) F(x,y,z)=(xyz)+(xy) 4) F(x,y,z)=x+(y+z)(x+y+z)(x+y+z) 5) F(w,x,y,z)=xz+xyz+wxz+wz 4 Using DeMorgan's law, write an expression for the complement of F(10 pts) 1) F(x,y)=xy+z 2) F(x,y,z)=((x+y)(x+z))xz+yz 5 Construct truth table for the following: (10 pts) 1) F(x,y,z)=xy+yz+yz+xz 2) F(x,y,z)=x(y+xz+yz) 6 The truth table of a JK flip-flop is given by Assume it is rising edge-triggered, which means the state Q will change on the rising edge of the clock signal, and the initial state of Q is 0 . Given the signal J and K, which change with time, draw the timing diagram for Q on the diagram below to show the changes as J and K change. ( 10pts) 7 The truth table of a D flip-flop is given by Again, assume it is rising edge-triggered, which means the state Q will change on the rising edge of the clock signal, and the initial state of Q is 0 . Given signal D as it changes with time, draw the timing diagram for Q on the diagram below to show its changes with respect to D. (5 pts) Page | 3