Design a Turing machine $($TM$)$ that performs addition of two binary numbers. Then implement the TM using python. The two binary numbers will be provided on a single tape, separated by the symbol $+,$ and in little$-$endian form $($the smallest number is located on the right side of the tape $).$ The TM$$s head will start at the rightmost position of the numbers.

Steps:

$1.$ Begin by defining the set of states Q$,$ the input alphabet $$ and the tape alphabet $.$

$2.$ Outline the process $($e$.$g$.,$ read one bit, move to the corresponding bit of the second number, change the state based on the sum, write the result, $...).$

$3.$ Create the state table and plot the associated state diagram.

$4.$ Implement this TM in python. Test your program to ensure it works as expected.

$5.$ Provide the working python implementation of your Turing Machine