Half precision floating point question -- smallest non-zero number
In this example, $2^{-10}$ is the mantissa, and $2^{-14}$ is the exponent.
For a fuller explanation of subnormal numbers in IEEE-754 floating point, see this previous answer.
Your example binary16 (i.e. half-precision) floating point number is a subnormal number because the exponent field is the &quot;all zeroes&quot; pattern. This means:

The significand field contains the fractional part of the mantissa, with an implicit &quot;0&quot; to the left of the binary point.
The exponent is set to $2^{-14}$. For binary32 (i.e. single precision) this would be $2^{-126}$ and for binary64 (i.e. double precision) it would be $2^{-1022}$.

So the number is $+0.0000000001_2 \times 2^{-14} = 2^{-24}$.