Design a combinational circuit with four input lines (A3A2A1A0) that represent a single BCD digit, and four output lines (B3B2B1B0) that generate the 9s complement of the input digit. Note that input combinations 1010, 1011, 1100, 1101, 1110, and 1111 do not correspond to legitimate binary-coded decimals; you should treat each of these combinations as a dont-care condition in your circuit design and implementation. Your circuit should also provide a fifth output E that indicates an error in the BCD: this output should be equal to a logic-1 whenever one of the six illegal combinations of inputs is detected.

Construct a truth table illustrating the behavior of your 9s complement circuit.

(B) Use Karnaugh maps to determine minimal sum-of-products expressions representing each of the five outputs (B₃B₂B₁B₀ and E).

(C) Design a circuit that uses two-input NOR gates to implement B₃.

(D) Design a circuit that uses an exclusive-OR gate to implement B₂.

(E) Verify that no gates are necessary to produce B₁.

(F) Design a minimal circuit that implements B₀.

(G) Design a circuit that uses two-input NAND gates to implement E.