A novel fault-model for regular and irregular parallel-prefix adders

In this paper a new fault-detection model, pair faults (pf), is presented to show that the entire 'O' carry-tree of Brent-Kung adder is testable contrary to Becker's proof. This model is also used to detect multiple faults for both regular and irregular carry-tree layouts. There are n+1 test patterns which can be applied (n is the operand width) through pipelining the primary inputs of the carry-tree. For this purpose, three new lemmas, one pf-model and their proofs are presented.