Topic: Digital Circuits
A Mealy system produces a '1' output if the input has been 'O' for at least two consecutive clocks followed immediately by two or more consecutive '1's. The minimum number of states for this system is
- A. 2
- B. 3
- C. 4
- D. 5
Answer: C. 4
Explanation: Let's define the minimum states required to track this sequence:
S0: Initial state (or consecutive 1s not meeting the condition). If 0, go to S1.
S1: One '0' seen. If 0, go to S2. If 1, return to S0.
S2: Two or more '0's seen. If 0, stay in S2. If 1, condition met partially, go to S3 and output 0.
S3: Two or more '0's followed by one '1' seen. If 1, output 1 and stay in S3 (since the condition 'two or more consecutive 1s' remains satisfied as long as 1s continue). If 0, the sequence breaks, go to S1 and output 0.
Because S3 correctly loops on itself for continuous 1s and outputs 1, the entire machine only requires these 4 states.