Four bits is a nibble and eight bits is a byte. Is there any formal or established nomenclature for a logical pairing of two bits?
Terminology for a logical pairing of 2 binary bits
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No, there is not any formal or established nomenclature for two-bit entities. But a variety of terms do exist, some of which are listed in the Jargon File, which says:
Emphasis mine.
For a two-bit quantity, ibid. says: