How did ancient Egyptian scribes multiply numbers by successive doubling?

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arithmetic A page from a first-grade workbook typical of “new math” might state: “Draw connecting lines from triangles in the first set to triangles in the second set. Are the two sets equivalent in number?”

Ancient Egyptian scribes performed multiplication using a method of successive doubling, which relied on the binary decomposition of numbers.

To multiply two numbers, such as 28 by 11, a scribe would construct a table of multiples of the first number (28) by powers of two (1, 2, 4, 8, etc.). The process follows these steps:

Construct a table: List the multiples of the multiplicand (28) corresponding to 1, 2, 4, 8, and so on.
Identify components: Determine which entries in the first column sum to the multiplier (11). In this case, 8 + 2 + 1 = 11.
Sum the results: Add the corresponding multiples from the table to find the final product. For 11 × 28, the scribe would add the values corresponding to 8, 2, and 1 (224 + 56 + 28), resulting in 308.1

For larger numbers, this method could be optimized by incorporating multiples of 10, 20, or higher powers of 10, which were easily calculated within the Egyptian decimal system.1