(Solved): Could you show the work and explanation for this 5. In a ternary number system, there are three digi ...

5. In a ternary number system, there are three digits: 0,1 , and 2. Table 1 define a ternary half-adder. Design a circuit that implements this half-adder using binary-encoded signals, such that two bits are used for each ternary digit. Let \( A=a_{1} a_{0}, B=b_{1} b_{0} \), and Sum \( =s_{1} s_{0} \); note that Carry is just a binary signal. Use the following encoding: \( 00=(0)_{3}, 01=(1)_{3} \), and \( 10=(2)_{3} \). Minimize the cost of the circuit. (5 points). Table-1