The Ancient Egyptian numerical system required arithmetic to be essentially additive. Multiplication and division were performed by a succession of doubling operations, using a method that developed over time into a technique known as duplation and mediation. To illustrate the technique we'll evaluate the product 23 × 14. We successively double 14, while at the same time halving 23, and keeping a record of whether or not the answer is odd.

Doubling Halving Odd?
1423yes
2811yes
565yes
1122 
2241yes

We now add the numbers in the doubling column that correspond to odd values in the halving column, and this gives us the answer we're looking for (14 + 28 + 56 + 224 = 322). This method, which is much simpler than long multiplication, for example, remains the basis for multiplication in computers. In fact, it is no coincidence (given today's understanding of mathematics) that the "Odd?" column actually gives us the binary expansion of 23. Treat each yes as a 1, and each no as a 0. Reading up the column then gives 10111, which is the decimal number 23 written in binary.

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