Stuck-at Fault Diagnosis of Four-bit Carry Look-ahead Adder by Shannon Expansion via Semi-tensor Product

In this paper, a stuck-at fault diagnosis algorithm is proposed for the four-bit carry look-ahead adder based on Shannon expansion and semi-tensor product. First, the algebraic representation of Shannon expansion is introduced via the semi-tensor product. Second, a sum-of-product four-bit carry look-ahead adder is given by a Python library for electronic design automation through fixing the order of input signals. Third, by the definition of stuck-at faults, the problem of stuck-at fault diagnosis is transformed into solving the system of linear equations based on the algebraic representation of Shannon expansion. Finally, the fault diagnosis of four-bit carry look-ahead adder is carried out for a special stuck-at fault case to validate the proposed algorithm.