A new method for synthesizing Single-Bit Reconfigurable Passive Electromagnetic Skins (1RP-EMSs) featuring advanced beam shaping capabilities is proposed. By using single-bit unit cells, the multi-scale problem of controlling 1RP-EMSs is formulated as a two-phase process. First, the macro-scale synthesis of the discrete surface current that radiates the electromagnetic (EM) field fitting user-designed requirements is performed by means of an innovative quantized version of the iterative projection method (QIPM). Successively, the meta-atom states of the 1RP-EMS are optimized with a customized implementation of the System-by-Design paradigm to yield a 1RP-EMS that supports such a feasible reference current. A representative set of numerical results is reported to assess the effectiveness of the proposed approach in designing and controlling single-bit meta-atom RP-EMSs that enable complex wave manipulations.