(Solved): please help! Task 1: 2-bit comparator Design and build a 2-bit inequality comparator. The inputs ( A ...

Task 1: 2-bit comparator Design and build a 2-bit inequality comparator. The inputs ( $$A$$ and $$B$$ ) are each 2-bit numbers. There are three output lamps (only one should be ON for each set of inputs): - Lamp $$X$$ indicates if $$A>B$$ - Lamp $$Y$$ indicates if $$A=B$$ - Lamp $$Z$$ indicates in $$A<B$$ Some tips: - Follow the steps of the design process (define objectives, define input/output variables, derive truth table, use Karnaugh Maps to simplify equations, draw logic diagram and fully test with LogicWorks) - Name your input variables $$A_1,A_0,B_1,B_0$$ - The final SOP equations should have some product terms with three literals. This is an issue simply because our AND chips only have 2-input gates. If you factor out a literal from a couple product terms, you can develop an equation that is easier to wire. - For example: $$Q^{?}{R}^{?}S+Q{R}^{?}T=R^{?}\left(Q^{?}S+QT\right)$$ - The SOP equation for $$Y$$ gets a little tedious. You could take advantage of the fact that $$Y=1$$ only if $$X=0$$ and $$Z=0$$ (in other words, if neither $$X$$ nor $$Z$$ are On) In report: - Describe the problem - All of these foundational components of the design: Variable definition Truth table Karnaugh Map that identifies simplest SOP equation (hint: not all input bits are needed!) Slightly modified equation to use 2-input gates Logic circuit