Multiplication of Decimal Numbers

GUIDE: Mathematics of the Discrete Fourier Transform (DFT). Multiplication of Decimal Numbers

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Multiplication of Decimal Numbers

Since decimal numbers are implicitly just polynomials in the powers of 10, e.g.,

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it follows that multiplying two numbers convolves their digits. The only twist is that, unlike normal polynomial multiplication, we havecarries. That is, when a convolution result exceeds 10, we subtract 10 from the result and add 1 to the digit in the next higher place.

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