CASE $2$:

Once upon a time, in a small village, there was a group of computer programmers who loved to

solve challenging problems. One day, they stumbled upon a unique language that consisted of

strings of $0\text{'}$s and $1\text{'}$s$.$ The language had some peculiar rules. Each string must start with $0,$ end with

$1,$ and contain an even number of $0\text{'}$s between them. For example, $010101$ and $00001111$ are both valid

strings in this language, but $0110$ and $0011$ are not.

The programmers were fascinated by this language and decided to create a program that could

generate all possible strings in this language. After several attempts, the team finally succeeded in

creating a program that could generate all the valid strings in this language. They ran the program

and were amazed to see thousands of strings that followed the language's rules. The team was

overjoyed with their success and decided to share their program with the world. The program

quickly became popular among computer programmers worldwide, and everyone began to use it to

generate strings in this unique language. The team received accolades and appreciation from all

corners for their remarkable achievement.

From that day onwards, the language of strings with $0\text{'}$s and $1\text{'}$s that start with $0,$ end with $1,$ and

have an even number of $0\text{'}$s in between became known as the "Even$-0\text{'}$s Language." And the team

that created the program to generate all possible strings in this language became famous as the

"Even$-0\text{'}$s Programmers."

Question $5$:

CO$3$

Considering the above scenario, design the Turing machine for the language in

Case $2.$