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Silicon tracking detectors can record the charge in each channel (analog ordigitized) or have only binary readout (hit or no hit). While there issignificant literature on the position resolution obtained from interpolationof charge measurements, a comprehensive study of the resolution obtainable withbinary readout is lacking. It is commonly assumed that the binary resolution is$\text{pitch}/\sqrt{12}$, but this is generally a worst case upper limit. Inthis paper we study, using simulation, the best achievable resolution forminimum ionizing particles in binary readout pixels. A wide range of incidentangles and pixel sizes are simulated with a standalone code, using the Bichselmodel for charge deposition. The results show how the resolution depends onangles and sensor geometry. Until the pixel pitch becomes so small as to becomparable to the distance between energy deposits in silicon, the resolutionis always better, and in some cases much better, than $\text{pitch}/\sqrt{12}$.

Ultimate position resolution of pixel clusters with binary readout for particle tracking