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In binary arithmetic, division by two can be performed by a bit shift operation that shifts the number one place to the right. This is a form of strength reduction optimization. For example, 1101001 in binary (the decimal number 105), shifted one place to the right, is 110100 (the decimal number 52): the lowest order bit, a 1, is removed.
Horner's method is a fast, code-efficient method for multiplication and division of binary numbers on a microcontroller with no hardware multiplier. One of the binary numbers to be multiplied is represented as a trivial polynomial, where (using the above notation) a i = 1 {\displaystyle a_{i}=1} , and x = 2 {\displaystyle x=2} .
Long division is the standard algorithm used for pen-and-paper division of multi-digit numbers expressed in decimal notation. It shifts gradually from the left to the right end of the dividend, subtracting the largest possible multiple of the divisor (at the digit level) at each stage; the multiples then become the digits of the quotient, and the final difference is then the remainder.
This page was last edited on 13 September 2019, at 14:21 (UTC).; Text is available under the Creative Commons Attribution-ShareAlike 4.0 License; additional terms may apply.
For example, in elementary arithmetic, one has (+) = + (). Therefore, one would say that multiplication distributes over addition . This basic property of numbers is part of the definition of most algebraic structures that have two operations called addition and multiplication, such as complex numbers , polynomials , matrices , rings , and fields .
It is frequently stated that arithmetic right shifts are equivalent to division by a (positive, integral) power of the radix (e.g., a division by a power of 2 for binary numbers), and hence that division by a power of the radix can be optimized by implementing it as an arithmetic right shift. (A shifter is much simpler than a divider.
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