draw the state diagram of a Turing Machine that will compute x + y, where x and y are given in unary representation. Assume that the non-blank portion of the input tape consists of x occurrences of ones (to represent x) followed by a $ sign and then y occurrences of ones with an infinite number of blanks on both sides of the non-blank portion of the tape. The non-blank portion of the output of your Turing Machine is expected to be x ones followed by the $ sign followed by y ones followed by the # sign followed by x + y ones. For example, if x = 5 and y = 7, then your input tape will be 11111$1111111, which produces the output tape 11111$1111111#111111111111 (with blanks on both sides of the non-blank portion).

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