Example of Russian-style multiplication. This algorithm multiplies natural numbe

Question

Example of Russian-style multiplication. This algorithm multiplies natural numbers. The inputs are A and B. We have one bit of notation to explain; the floor function |_x_| returns the greatest integer less than or equal to x. (The assignment (Challenge) is below 7). Let Astep = A snd let Bstep = B. Start a column by writing 0 at the top. If Astep is odd, then write Bstep in the column; otherwise, continue. Replace Astep with |_Astep divided by 2_|. Replace Bstep with Bstep + Bstep. If Astep = 1, then write Bstep in the column and go to step 7; otherwise, go to step 3. Sum the column. ASSIGNMENT Challenge: Understand the algorithm for Russian multiplication in the example above: Execute the algorithm using A = 12 and B = 7. Now choose two different values for A, B and execute the algorithm again. When do you write down Bstep and when not? When you sum the column, what multiple of B (how many copies of B) do you obtain? Does this have anything to do with binary numbers? How exactly does this algorithm give the same result as usual multiplication?

Explanation / Answer

http://www.networksorcery.com/enp/data/encryption.htm

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