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A carry-save adder [1] [2] [nb 1] is a type of digital adder, used to efficiently compute the sum of three or more binary numbers. It differs from other digital adders in that it outputs two (or more) numbers, and the answer of the original summation can be achieved by adding these outputs together.
Kummer's theorem states that the number of carries involved in adding two numbers in base is equal to the exponent of the highest power of dividing a certain binomial coefficient. When several random numbers of many digits are added, the statistics of the carry digits bears an unexpected connection with Eulerian numbers and the statistics of ...
It is based on the remark that every integer is the difference of two natural integers and that two such differences, a – b and c – d are equal if and only if a + d = b + c. So, one can define formally the integers as the equivalence classes of ordered pairs of natural numbers under the equivalence relation
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The first version of Sumatra PDF, designated version 0.1, was based on Xpdf 0.2 and was released on 1 June 2006. It switched to Poppler from version 0.2. In version 0.4, it changed to MuPDF for more speed [4] and better support for the Windows platform. Poppler remained as alternative engine for a time, and from version 0.6 to 0.8 it was ...
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