In a ternary number system there are three digits: 0, 1, and 2. Figure P3.3 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; 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.

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AB Carry 00 01 02 10 11 12 20 21 22 0 0 0 0 0 1 0 1 1 Sum 0 1 2 1 2 0 2 0 1