We report a broadband digital electro-optical switch, based upon a multi-stage Mach-Zehnder lattice design in silicon-on-insulator. A digital switching response is demonstrated, engineered through apodization of the coupling coefficients between stages. The digital switching behavior results in crosstalk lower than -15 dB for drive-voltage noise levels in excess of 300 mV(pp), which exceeds the noise tolerance of a conventional single-stage Mach-Zehnder switch by more than six-fold. In addition, the digital design enables a larger maximum 'on'-state extinction (below -26 dB) and lower 'on'-state free-carrier-induced insertion loss (less than 0.45 dB) than that of the single-stage switch. The noise-tolerant, low-crosstalk switch can thus play a key role within CMOS-integrated reconfigurable optical networks operating under noisy on-chip conditions.