You are designing a sequence detector to detect the overlapping pattern "1011" from a serial input stream. What is the minimum number of flip-flops required to implement this as a strictly Moore state machine?
A Moore machine for overlapping "1011" requires states for each phase of detection plus the reset state: S0 (Reset/None), S1 (Found '1'), S2 (Found '10'), S3 (Found '101'), and S4 (Found '1011', outputs 1). This totals 5 states. The minimum number of flip-flops required to encode N states is ceil(log2(N)). Therefore, ceil(log2(5)) = 3 flip-flops.
