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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.
It is part of the standard algorithm to add numbers together by starting with the rightmost digits and working to the left. For example, when 6 and 7 are added to make 13, the "3" is written to the same column and the "1" is carried to the left. When used in subtraction the operation is called a borrow.
He designed the machine to add and subtract two numbers directly and to perform multiplication and division through repeated addition or subtraction. Pascal's calculator was especially successful in the design of its carry mechanism , which adds 1 to 9 on one dial, and carries 1 to the next dial when the first dial changes from 9 to 0.
If an adding circuit is to compute the sum of three or more numbers, it can be advantageous to not propagate the carry result. Instead, three-input adders are used, generating two results: a sum and a carry. The sum and the carry may be fed into two inputs of the subsequent 3-number adder without having to wait for propagation of a carry signal.
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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
[1] [2] All functions use floating-point numbers in one manner or another. Different C standards provide different, albeit backwards-compatible, sets of functions. Most of these functions are also available in the C++ standard library, though in different headers (the C headers are included as well, but only as a deprecated compatibility feature).
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