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The term 'the binary' is correct and usable in written English
It is generally used to refer to a dichotomous concept such as gender or a two-option scenario, for example: "The binary of male/female reveals how gender is a constructed concept."
Dictionary
the binary
noun
The bijective base-2 numeral system, which uses only the digits 0 and 1.
Exact(60)
"The binary neutron stars are like the piccolos," Reitze said.
The binary nature of the debate is worrying some progressives.
I wondered if the older diners would be satisfied with the binary choices on the menu.
The binary classifications of sports might have a difficult time accommodating the continuum of human sexuality.
(It involves counting in the binary system; a full explanation can be found on Wikipedia).
His story will go beyond the binary, outside the algorithms, away from the median.
The binary digits could be used to represent words, sounds, images -- perhaps even ideas.
The I-Ching represents the binary poles of reality as Yin and Yang.
I broadly sympathise with Williams's despair at the "binary arguments" that parents are embroiled in.
To an extent, their preoccupation with the binary reflects the influence of post-structuralist philosophy.
Profanity is a theological category generated by the binary opposition of sacred and profane.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com