An all-optical computer has remained an elusive concept. To construct a practical computing primitive equivalent to an electronic Boolean logic, one should utilize nonlinearity that overcomes weaknesses that plague many optical processing schemes. An advantageous nonlinearity provides a complete set of logic operations and allows cascaded operations without changes in wavelength or in signal encoding format. Here we demonstrate an all-optical majority gate based on a vertical-cavity surface-emitting laser (VCSEL). Using emulated signal coupling, the arrangement provides Bit Error Ratio (BER) of 10-6 at the rate of 1 GHz without changes in the wavelength or in the signal encoding format. Cascaded operation of the injection-locked laser majority gate is simulated on a full adder and a 3-bit ripple-carry adder circuits. Finally, utilizing the spin-flip model semiconductor laser rate equations, we prove that injection-locked lasers may perform normalization operations in the steady-state with an arbitrary linear state of polarization.