The 8, 4,2,1 BCD code is similar to the 8-4-2-1 BCD code,

Chapter 16, Problem 16.10

(choose chapter or problem)

The 8, 4,–2,–1 BCD code is similar to the 8-4-2-1 BCD code, except that the weights are negative for the two least significant bit positions. For example, 0111 in 8, 4,−2,−1 code represents

                                                \(8 \times 0 + 4 \times 1 + (−2) \times 1 + (−1) \times 1 = 1\)

Design a Mealy sequential circuit to convert 8, 4,–2,–1 code to 8-4-2-1 code. The input and output should be serial with the least significant bit first. The input X represents an 8, 4,–2,–1 coded decimal digit and the output Z represents the corresponding 8-4-2-1 BCD code. After four time steps the circuit should reset to the starting state regardless of the input sequence. Design your circuit using three D flip-flops, NAND gates, and NOR gates. Any solution which is minimal for your state assignment and uses eight or fewer gates is acceptable. (Assign 000 to the reset state.)

Test Procedure: First, check out your state table by starting in each state and making sure that the present output and next state are correct for each input. Then, starting in the reset state, determine the output sequence for each of the 10 possible input sequences and make a table.