Update addition_without_arithmetic.py

[Cgarg547]

I have made few changes for more clarity.

1. Wrote comments making the logic clearer
2. Changed the var name from c to carry for more clarity

Describe your change:

• [ ] Add an algorithm?
• [ ] Fix a bug or typo in an existing algorithm?
• [ ] Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request.
• [x] Documentation change?

Checklist:

• [ ] I have read CONTRIBUTING.md.
• [ ] This pull request is all my own work -- I have not plagiarized.
• [ ] I know that pull requests will not be merged if they fail the automated tests.
• [ ] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
• [ ] All new Python files are placed inside an existing directory.
• [ ] All filenames are in all lowercase characters with no spaces or dashes.
• [ ] All functions and variable names follow Python naming conventions.
• [ ] All function parameters and return values are annotated with Python type hints.
• [ ] All functions have doctests that pass the automated testing.
• [ ] All new algorithms include at least one URL that points to Wikipedia or another similar explanation.
• [ ] If this pull request resolves one or more open issues then the description above includes the issue number(s) with a closing keyword: "Fixes #ISSUE-NUMBER".