Bino's Model of Multiplication
Bino's Model of Multiplication is a new and correct model of multiplication process in general. The main motivation towards developing Bino’s model of multiplication is to find a way of doing multiplication of three or more numbers together at one go, in the same way as we do in addition of three or more numbers, so that we can perform multiplication eaier and faster. Also, this new model of multiplication is a general model for multiplication of numbers, polynomials and arrays (of numeric data). The multiplication of two arrays is generally studied in signal processing as linear convolution (a mathematical expression for the filtering operation), an indispensable process in signal processing. In other words, Bino’s model of multiplication can very well represent the filtering operation. Besides allowing us to perform multiplication in an easier and faster way, this model of multiplication also enables us to generalize the binomial expansion to trinomial, quadrinomial (and other higher order) expansions. Consequently, it leads to generalization of the Pascal triangle to convolution triangles of various base lengths. Convolution triangles may also be useful for designing various types of averaging filters.
A paper on Bino's Model of multiplication in word file format is provided here. This paper was accepted in the WSES Multiconference on Applied and Theoritical Mathematics, Athens, Greece, 2001. MS-Word package is required to view this file.
Two multi-digit numbers Multiplication
Example on Multiplication of two large numbers
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