Prerequisite – Turing Machine

A number is represented in binary format in different finite automatas like 5 is represented as (101) but in case of addition using a turing machine unary format is followed. In unary format a number is represented by either all ones or all zeroes. For example, 5 will be represented by a sequence of five zeroes or five ones. 5 = 1 1 1 1 1 or 0 0 0 0 0. Lets use zeroes for representation.

For adding 2 numbers using a Turing machine, both these numbers are given as input to the Turing machine separated by a “c”.

**Examples –** (2 + 3) will be given as 0 0 c 0 0 0:

Input : 0 0 c 0 0 0 // 2 + 3 Output : 0 0 0 0 0 // 5 Input : 0 0 0 0 c 0 0 0 // 4 + 3 Output : 0 0 0 0 0 0 0 // 7

**Approach used –**

Convert a 0 in the the first number in to X and then traverse entire input and convert the first blank encountered into 0. Then move towards left ignoring all 0’s and “c”. Come the position just next to X and then repeat the same procedure till the time we get a “c” instead of X on returning. Convert the c into blank and addition is completed.

**Steps –**

**Step-1:** Convert 0 into X and goto step 2. If symbol is “c” then convert it into blank(B), move right and goto step-6.

**Step-2:** Keep ignoring 0’s and move towards right. Ignore “c”, move right and goto step-3.

**Step-3:** Keep ignoring 0’s and move towards right. Convert a blank(B) into 0, move left and goto step-4.

**Step-4:** Keep ignoring 0’s and move towards left. Ignore “c”, move left and goto step-3.

**Step-5:** Keep ignoring 0’s and move towards left. Ignore an X, move left and goto step-1.

**Step-6:** End.

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