This paper studies the identification of infinite impulse response (IIR) systems with binary-valued measurements. The key to our approach is to recast the initial identification problem into an identification problem in the set-membership framework. This enables us to identify the system using an identification algorithm devoted to IIR systems in such a framework. Although the proposed algorithm is designed for noise free data, an analysis is provided in the presence of noise, and illustrative examples are provided to demonstrate the effectiveness of the algorithm.