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In base 2, long multiplication reduces to a nearly trivial operation. For each '1' bit in the [[wikt:multiplier|multiplier]], shift the [[wikt:multiplicand|multiplicand]] an appropriate amount and then sum the shifted values. Depending on computer processor architecture and choice of multiplier, it may be faster to code this algorithm using hardware bit shifts and adds rather than depend on multiplication instructions, when the multiplier is fixed and the number of adds required is small.
This [[algorithm]] is also known as peasant multiplication, because it has been widely used among those who are classified as peasants and thus have not memorized the [[multiplication table]]s required by long multiplication.<ref name=":0">{{Cite web|url=https://www.cut-the-knot.org/Curriculum/Algebra/PeasantMultiplication.shtml|title=Peasant Multiplication|last=Bogomolny|first=Alexander|website=www.cut-the-knot.org|access-date=2017-11-04}}</ref> The algorithm was also in use in ancient Egypt.<ref
On paper, write down in one column the numbers you get when you repeatedly halve the multiplier, ignoring the remainder; in a column beside it repeatedly double the multiplicand. Cross out each row in which the last digit of the first number is even, and add the remaining numbers in the second column to obtain the product.
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