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The paper deals with fundamentals of systems of Boolean functions called multi-output functions (MOFs). A new approach to representing MOFs is introduced based on a Generalized If-Then-Else (GITE) function. It is shown that known operations on MOFs may be expressed by a GITE function. The GITE forms the algebra of MOFs. We use the properties of this algebra to solve an MOF-decomposition problem. The solution provides a compact representation of MOFs.

A Generalized If-Then-Else Operator for the Representation of Multi-Output Functions