Multiplication of Decimal Numbers

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

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

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Order a Hardcopy of Mathematics of the DFT

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written by Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.