Digital logic

1. Simplify the following function: F(X,Y,Z)=(2,3,4,6)+d(0,5) A) F=(X+Y+Z)Y B) F=(X+Y)(X+Z) C) F=Z(X+Y) D) F=XY+XY+XZ E) F=YZ+XYZ F) F=ZX+Y 2. For the circuit shown below, if A1>B0, which of decoder output lines may be active? Hint: You don't know the value of A0 and B1 4. For the circuit shown below, if you know that X=1 and YCin=1 What is the Boolean expression of F ? 5. If the present stante of a JK fip flop cquals 1(Q(0)=1 ), what will be the value of the next state (Qt t+1 in A) Q(t+1)=0 B) Q(t+1)=Q(t) C) Q(t+1)=Q(c) D) Q(t+1)=K E) Q(t+1)=JK F) None of the above \begin{tabular}{|c|c|c|} \hline \multicolumn{3}{|c|}{\begin{tabular}{l} 5. An active low SR batch will renember the value I when the SR values are as follow: \\ A) SR=00 then SR=10 \end{tabular}} \\ \hline D) SR=11 the S & B) SR=01 then SR=10 & C) SR=00 then SR=11 \\ \hline 1) 3x11tan3x=00 & E) SR=01 then SR=11 & F) Nobe of the above \\ \hline \end{tabular} 7. The function F(X,Y,Z) is implemented using 21MUX as follows S=X,I0=Y+Z, and I1= XeYeZ which of the following is the curtect representatica of F(A,B,C) ? A) F(X,Y,2)=(0,3,4,7) B) F(X,Y,Z)=Z(1,3,6,7) C) F(X,Y,Z)=(4,7) D) F(X,Y,2)=(1,5,6) ) F(X,Y,Z)=(2,6,7) f) Nore of the abore 8. Given the following timing diagram for the circuit on the side, if you know that Q=1 for t510. What is the simplest Boolean expression of F(A1,A0,B2,B1,B0) ? A) F=A1A0+B2B1B0 B) F=(A1A0)(B2+B1+B0) C) F=A1A0B2B1B0 D) F=A1A0B2B1 E) F=(A1+A0)(B2+B1+B0) F) None of the above 10. What is the most simplified Boolean expression of F(A,B), knowing that A is the MSB of inputs? A) F=m0+m2+m3 B) F=AB+AB C) F=AB D) F=M0M2M3 E) F=A+B F) None of the above 11. Assume that we redesigned the 4 -bit adder/subtractor studied on class. The adder/subtractor now can perform B+A and BA, if you know that A=0010,B=0101 and M=1, then find S, Cout and OV (overflow) values. A) S=1101,OV=0, Cout =0 B) S=1001,OV=0, Cout =1 C) S=0011,OV=0, Cout =1 D) S=0001,OV=0, Cout =1 E) S=1100,OV=1, Cout =0 F) None of the above 13. I4 points) Analyze the following cirouit by finding ite truth table of P(X,Y,Z) Analyze the circuit shown below F(A,B,C)= 10. For the 42 priority encode- -hinun helow. if F1F001, determine the value of inputs D0=D1=D2=D3= P1(X,Y,Z)y F1(X,Y,Z)= 8. For the circut shown below, what is the value of output Z if DF0 as shown in the circuif Hint You should not construct any mith table KMAP. Q2/3points]-Designthefollowingfunctionusing2-1MrXwherecistheselectionlineF(x,y,Z)=(0,4,5)+d(2,7) F(x,y,Z)=(0,4,5)+d(2,7) Part 2 (design questions): 2. If the second input is less than itie decimal value three, then the cuiput is A a of the inith table roms are already filled to asistyou