Final answer:
To design a logic circuit with two inputs and two outputs based on given conditions, create a truth table, simplify the logic expressions using boolean algebra, and optimize the solution using boolean algebra laws and Karnaugh maps.
Step-by-step explanation:
To design a logic circuit that takes two 2-bit unsigned numbers A and B as input and has two outputs X and Y, we first need to create a truth table based on the given conditions. The truth table will list all possible values for A and B and the corresponding values for X and Y based on the conditions x=1 if (A+B)=2 and y=1 if (A+B)>2.
After creating the truth table, we can simplify the logic expressions for X and Y using boolean algebra. By simplifying the expressions, we can reduce the number of logic gates required for the circuit, resulting in an optimized solution. Once the simplified expressions are obtained, we can design the logic circuit using the optimized expressions and gates such as AND, OR, and NOT gates.
To obtain the optimized solution, we can use boolean algebra laws such as distributive, commutative, and identity laws. We can also use Karnaugh maps to simplify the expressions further by identifying groups of 1s and creating minimal logic expressions from those groups. By applying these optimization techniques, we can reduce the number of gates required and improve the efficiency of the circuit.