You're going a bit off the rails of what IEEE 754 defined, historically.
However, the new (2018) standard comes to the rescue with some clarity:
NOTE 3—For binary formats, the precision p should be at least 3, as some numerical properties do not hold for lower precisions.
Similarly, emax should be at least 2 to support the operations listed in 9.2.
So the significand should have at least three bits (one of which may be implicit), separate from the need to encode qNaN and sNaN.