Detailed analyses have been presentd for a basic single-electron-logic-cell consisting of two single-electron-transistors (SETs) in series. The interconnection between two SETs has been treated as a coulomb island and the joint probability density function of all three coulomb islands (two from the SETs and one form the interconnection) has been exactly calculated. The average number of electrons in each coulomb island and the steady-state ouptut voltage have been calculated and analyzed.