Binary diagonally noncomputable function ($f:\mathbb{N}\to \{0,1\},{\phi }_e(e)\downarrow ⟹f(e)\ne {\phi }_e(e)$)

A total binary-valued function is diagonally noncomputable if it differs from each defined diagonal value in an effective enumeration of partial computable functions. Nonbinary diagonal outputs are automatically different. No such function is computable: its own program index would contradict the defining condition. Choosing the opposite bit at every defined binary diagonal value proves existence without supplying a computable procedure.