Question: S. lets generalize to compute 2. In exponentiation we multiply things together as opposed to adding them, so we generalize6. the technique by Replace adding

 S. lets generalize to compute 2". In exponentiation we multiply things

S. lets generalize to compute 2". In exponentiation we multiply things together as opposed to adding them, so we generalize6. the technique by Replace adding with multiplying Replace doubling with squaring. In other words, replace "multiply by 2" with "power of 2." Here are the calculations. We start with a running product, and we initialize that with 1. 13 is odd, so we multiply the second column into our running product giving 2. Then we halve 13 and square 2. exp base Next step: 6 is even so don't multiply into our running total. Then halve the 6 and square the 4 to get 16 16 1 256 65546 32 8192 Now 3 is odd, so multiply 16 into the running product to give 32. Then halve the first column and square the second. Final step: 1 is odd, so multiply 256 by 32 to give 8192, which is our final answer. The cool thing is that the proof we have above works for this too. Our invariant is now: BA.R-E where E is our desired exponentiation. Write the Pseudocode, Algorithm to implement the algorithm above

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