The Air-To-Fuel ratio (AFR) is a crucial parameter to ensure good quality combustion and high catalyst efficiency. This work addresses the problem of determining continuous-time estimates of AFR in turbocharged Spark Ignition (SI) engines on the basis of only binary (on/off) sparse measurements of the exhaust gas Oxygen determined by using a HEGO (Heated Exhaust Gas Oxygen) sensor placed at the catalytic converter input in place of a more expensive linear UEGO (Universal Exhaust Gas Oxygen) sensor, as nowadays standard in commercial cars. In this context, the HEGO sensor, providing at its output terminal only two voltage values, can be considered a binary sensor with irregular and sparse measurements in that the useful information in only present at the instants of the on/off and off/on transitions. The theory of linear hybrid observers with quantized outputs is used to single out an estimation scheme based on a recursive least-squares algorithm. A detailed convergence analysis of the state reconstruction error is also provided. The proposed hybrid observer scheme is then used in a PI control loop finalized to maintain the AFR close to a desired value. The effectiveness of the proposed method is demonstrated by numerical simulations.