  Contextuality is a fundamental feature of quantum theory and is necessary for
quantum computation and communication. Serious steps have therefore been taken
towards a formal framework for contextuality as an operational resource.
However, the most important component for a resource theory - a concrete,
explicit form for the free operations of contextuality - was still missing.
Here we provide such a component by introducing noncontextual wirings: a
physically-motivated class of contextuality-free operations with a friendly
parametrization. We characterize them completely for the general case of
black-box measurement devices with arbitrarily many inputs and outputs. As
applications, we show that the relative entropy of contextuality is a
contextuality monotone and that maximally contextual boxes that serve as
contextuality bits exist for a broad class of scenarios. Our results complete a
unified resource-theoretic framework for contextuality and Bell nonlocality.
