Logic Design Word Problem
While Ultron wreaked havoc to New York city, Tony Stark, Hawk Eye & Black-Widow were injured while heroically capturing Ultron, Quick-Silver & Scarlet-Witch. They have put them in 3 different cells named U, Q and S respectively (after their initials). With three of the Avengers injured, and Thor and Captain America having no knowledge of Logic Design, it is left with Hulk to design the Logic Circuit used for questioning each of the three villains. You have to help Hulk design the logic for questioning (without angering him ), while he does all the heavy lifting for your hardware.
The questioning is led by Tony, Nick Fury & Captain America as follows:
• Tony Stark is in charge of deciding which villain will be interrogated next, or if no villain should be questioned at the moment. To do that, Tony encodes his choice using a 2-bit unsigned integer T1T0 like this:
o 00 if no villain should be questioned,
o 01 for Ultron,
o 10 for Quick-Silver, and
o 11 for Scarlet-Witch.
• Nick Fury uses the button N to signal whether he wants to question (1) or not (0) the particular villain Tony has chosen.
• Captain America uses the button C to tell whether he wants to question (1) or not (0) the particular villain Tony has chosen.
• Questioning can only start when the corresponding link to a villain is active (U = 1 for Ultron, Q= 1 for Quick-Silver, and S = 1 for Scarlet-Witch.)
Since our heroes are complicated, the rules to activate the interrogation links are as follows:
• When Tony Stark's choice is 00, we cannot talk to any of the villains. (U=Q=S=0)
• When Tony Stark's choice is 01, and only Nick wants to question (N=1, C=0), the link to Ultron goes active (U=1, Q=S=0). Otherwise no interrogation will take place. (U=Q=S=0)
• When Tony Stark's choice is 10, and only Captain America wants to question (C=1, N=0), the link to Quick-Silver goes active (Q=1, U=S=0). Otherwise no interrogation will take place. (U=Q=S=0)
• When Tony's choice is 11, and Nick, Captain America, or both, want to question (N=1 or C=1), the link to Scarlet-Witch goes active (S=1, U=Q=0). If both Nick and Captain America do not want to question Scarlet-Witch (N=C=0), no interrogation will take place. (U=Q=S=0)
Based on this description, you need to design a circuit for questioning:
1. Design the desired truth table (inputs T1, T0, N, C) for the outputs U, Q and S.
2. Use a Karnaugh map to reduce the logical expressions for the functions U, Q and S to a minimal SOP form. Show your work.
3. Draw the complete logic schematic circuit diagram for your system, with inputs, T1, T0, N, C (and their complements) entering on the left side, and outputs U, Q and S on the right side.