This paper investigates the application of Shannon (BDD) circuits, that feature interesting low-power capabilities, to the design of self-checking functional units. A technique is proposed that, by using a time redundancy approach, makes this kind of circuits totally self-checking with respect to stuck-at faults. For a set of possibly used pass-transistor- based CMOS implementations, we show that the totally self-checking or the strongly fault secure properties hold for a wider set of realistic faults, including transistors stuck-open/on and bridgings.