csa-notes - Carry-Save Addition Prof Loh CS3220 Processor...

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Carry-Save Addition Prof. Loh CS3220 - Processor Design - Spring 2005 February 2, 2005 1 Adding Multiple Numbers There are many cases where it is desired to add more than two numbers together. The straightforward way of adding together m numbers (all n bits wide) is to add the first two, then add that sum to the next, and so on. This requires a total of m - 1 additions, for a total gate delay of O ( m lg n ) (assuming lookahead carry adders). Instead, a tree of adders can be formed, taking only O (lg m · lg n ) gate delays. Using carry save addition, the delay can be reduced further still. The idea is to take 3 numbers that we want to add together, x + y + z , and convert it into 2 numbers c + s such that x + y + z = c + s , and do this in O(1) time. The reason why addition can not be performed in O (1) time is because the carry information must be propagated. In carry save addition, we refrain from directly passing on the carry information until the very last step. We will first illustrate the general concept with a base 10 example. To add three numbers by hand, we typically align the three operands, and then proceed column by column in the same fashion that we perform addition with two numbers. The three digits in a row are added, and any overflow goes into the next column. Observe that when there is some non-zero carry, we are really adding four digits (the digits of
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This note was uploaded on 02/04/2012 for the course COMPUTER 101 taught by Professor Ahmed during the Summer '11 term at alamo.edu.

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csa-notes - Carry-Save Addition Prof Loh CS3220 Processor...

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