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In order to increase computing accuracy in multiple stages computing architecture, a novel stochastic fusion adder has been proposed, in which a new mathematical method, named hypergeometric decomposition, was developed to analyze the property of the proposed adder. It is shown that the proposed algorithm has much higher precision than the traditional one. By designing a stochastic DFT architecture based on this enhanced stochastic adder, all the advantages of stochastic computing were merged into DFT computing domain, and the DFT implementation also proves the successful design of this novel fusion stochastic adder. [ABSTRACT FROM AUTHOR]