Using Logisim$-$evolution Please create the design. I will send you my design by text and I also provided the instructions for you to see how the design is made $($the instructions are the image$).$ My design follows all the instructions provided in the image I included, I just please need you to create the design for me using my design my format$/$my work.

My design:

Step $1$:

Design a FSM to detect the sequence $000$ twice without overlap.

One possible solution to meet the design constraints is to use a Mealy FSM with four states: S$0,$ S$1,$ S$2,$ and S$3.$ The input X is fed into a $3-$bit shift register.

In state S$0,$ the output Z is $0$ and the shift register is cleared. If X is $0,$ the FSM transitions to state S$1.$ Otherwise, it stays in state S$0.$

In state S$1,$ X is shifted into the register. If the register contains the sequence $00$X$,$ where X is the last bit shifted in$,$ the FSM transitions to state S$2.$ Otherwise, it transitions back to state S$0.$

In state S$2,$ X is shifted again. If the register contains the sequence $000,$ the FSM transitions to state S$3.$ Otherwise, it transitions back to state S$1.$

In state S$3,$ the output Z is $1,$ indicating the detection of the sequence $000.$ The shift register is cleared, and the FSM transitions back to state S$0.$

This FSM detects the sequence $000$ twice without overlap.

Explanation:

Design a FSM to detect the sequence $000$ twice without overlap.

Step $2$:

Extend the FSM to detect the sequence $111$ once after detecting the $000$ sequence twice.

To extend the FSM to detect the sequence $111,$ we can introduce two new states: S$4$ and S$5.$

In state S$0,$ the output Z is $0$ and the shift register is cleared. If X is $0,$ the FSM transitions to state S$1.$ Otherwise, it stays in state S$0.$

In state S$1,$ X is shifted into the register. If the register contains the sequence $00$X$,$ where X is the last bit shifted in$,$ the FSM transitions to state S$2.$ Otherwise, it transitions back to state S$0.$

In state S$2,$ X is shifted again. If the register contains the sequence $000,$ the FSM transitions to state S$3.$ Otherwise, it transitions back to state S$1.$

In state S$3,$ the output Z is $1,$ indicating the detection of the sequence $000.$ The shift register is cleared, and the FSM transitions to state S$4.$

In state S$4,$ X is shifted into the register. If the register contains the sequence $1$XX$,$ where XX are the last two bits shifted in$,$ the FSM transitions to state S$5.$ Otherwise, it transitions back to state S$4.$

In state S$5,$ the output Z is $1,$ indicating the detection of the sequence $111.$ The shift register is cleared, and the FSM transitions back to state S$0.$

This extended FSM alternates between detecting the sequence $000$ twice and then the sequence $111$ once.

Explanation:

Extend the FSM to detect the sequence $111$ once after detecting the $000$ sequence twice.

Final Answer:

The FSM design described in steps $1$ and $2$ meets the design specifications and constraints provided. It uses a total of $6$ flip$-$flops $(4$ for the shift register, and $2$ for the state representation$).$ The gate count is minimized by utilizing the Mealy FSM model and carefully designing the state transitions based on the input sequence conditions. This design can be implemented in LogiSim and verified for its intended functionality.

The instructions for the assignment are in the image provided, again my work follows these instructions and I provided the image for you to have a general idea of how the design should look. Thank you.