Consider the language

$L=\{w$#$1^n|w,nin{N}^{+},wis$ a binary encoding $ofn\}$

Give an algorithmic level description of a Turing machine $M$ which

decides $L.$

Prove that $M$ halts for any input.

Prove that $M$ accepts all and only the strings in $L.$

Please help me with the three parts. Try to be as rigorous as possible. I will provide thumb up$!$