Question

A Mealy sequential circuit has one input X and one output Z. The output is high if and only if the most recent input, combined with the preceding three inputs represent the decimal powers of 2(X=2₁₀,4₁₀,8₁₀). Note that 010 is not included. Assume the most significant bits are received first. Derive a state table for the circuit. Reduce the state table if possible.

Answer 1

The task involves creating and reducing a state table for a Mealy sequential circuit that outputs high for bit sequences representing the decimal powers of 2. A state table is constructed with transitions based on input X and output Z is high for specific sequences, except for 010. State reduction techniques can further simplify the circuit.

Step-by-step explanation:

The question refers to the design of a Mealy sequential circuit which outputs high for a sequence of bits corresponding to the decimal powers of 2, excluding 010. This task involves digital logic and state machine design, which is an engineering and computer science concept. First, we need to construct a state diagram or state table based on the specified condition and then proceed to minimize the states if possible. The possible valid input sequences representing the decimal powers of 2 in binary are 001 (two), 010 (four), and 100 (eight).

To create the state table, we enumerate states for each sequence of three bits, defining transitions based on the input X. The output Z is high when the state corresponds to one of the sequences, except for 010 which should not produce a high output. The state table will contain columns for the current state, next state (with X=0 and X=1), and the output Z. After creating the table, we can use state reduction techniques to minimize the number of states if there are equivalent states.