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In this paper, on the basis of the Monte Carlo simulation, we demonstrate a method to realize logical operations by the use of the single-electron charge-induced signal transmission (CIST) circuit which we have proposed previously. First, we propose three new-type signal transmission circuits. Then, we demonstrate through construction of a NAND circuit and a full-adder circuit on the basis of the Monte Carlo simulation that we can construct any logic circuit by the use of these circuits. Since the CIST circuit can perform any logical operation and can transmit the state of the presence or absence of an electron and a hole as a binary signal over long distance during one clock cycle bidirectionally, these CIST circuits are expected to be applied to integrated circuit devices as a new circuit construction method.