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Big-theta: Traditional addition and multiplication logic

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Use big-theta notation to classify the traditional grade school algorithms for addition and multiplication. That is, if asked to add two numbers each having n-digits, how many individual additions must be performed? If asked to multiply two n-digit numbers, how many individual multiplications are required?

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To add two n digits numbers, we will need to perform
- minimum n individual additions, one at each digit position, when no carry results from any addition.
- maximum (2n - 1) ...

Solution Summary

Solution assumes familiarity with big-theta notation, and gives a brief explanation, more like a guidance to student.