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This paper presents a necessary and sufficient condition under which a discrete-time switched affine (SWA) state space model admits equivalent representations in the class of SWA input-output models. In particular, it is shown that observability is not a necessary requirement for input-output realization of SWA models. When an equivalent input-output representation exists, a constructive procedure is presented to derive both its parameters and the switching constraints. Numerical examples illustrate and motivate the presented equivalence result.