The dynamics of all-optical switching in C60 has been theoretically analyzed based on the principle of nonlinear intensity-induced excited-state absorption to achieve high contrast and fast switching. The transmission of a cw probe laser beam at 885 nm corresponding to the peak absorption of the S1 state through C60 in toluene is switched by a pulsed pump laser beam at 532 nm that excites molecules from the ground state. Switching characteristics are shown to be sensitive to the variation of pump pulse width, peak pumping intensity, thickness of the medium, intersystem crossing time between the S1 and T1 states and the absorption cross section of the S1 state at a probe wavelength, and their effect are analyzed in detail. It is shown that the transmission of the probe beam can be completely switched off (100% modulation) by the pump beam at a pump intensity of 100 MW/cm2 and a pulse width 1.5 ns, with switch on and off times of 2.5 and 7.5 ns, respectively. The results are used to design all-optical NOT and the universal NOR and NAND logic gates with multiple pump laser pulses, which are the basic building blocks of computing circuits.