All-optical switching has been theoretically analyzed in the 3,3′-diethyl-2,2′-thiatricarbocyanine iodide (DTTCI) carbocyanine dye that exhibits large excited-state absorption to achieve high contrast and fast switching. Switching has been analyzed both ns and ps pump pulse widths. It is shown that there is an optimum value of concentration for given peak pump intensity at which maximum modulation can be achieved. We can get 93.84% modulation of transmission of a CW probe laser beam at 532 nm at peak pumping intensity of 500 kW/cm² at 763 nm, with Δt=1 ns and concentration of 80 μM in alcohol, resulting in switch-off and on time of 2 ns and 8 ns, respectively. The results have been also used to design all-optical NOT and the universal NOR and NAND logic gates with multiple pump laser pulses.