In a ternary number system (i. e., base 3) there are three digits: 0, 1 and 2. The following table defines 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 = a1a0, b = b1b0, and Sum = s1s0; 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. AB Carry Sum
00 0 0
01 0 1
02 0 2
10 0 1
11 0 2
12 1 0
20 0 2
21 1 0
22 1 1

b. Extend the above concept to design a full-ternary adder circuit.