Half precision floating point question -- smallest non-zero number There's a floating point question that popped up and I'm confused about the solution. It states that

IEEE 754-2008 introduces half precision, which is a binary
floating-point representation that uses 16 bits: 1 sign bit, 5
exponent bits (with a bias of 15) and 10 significand bits. This format
uses the same rules for special numbers that IEEE754 uses. Considering
this half-precision floating point format, answer the following
questions: ....
What is the smallest positive non-zero number it can represent?

The answer says:
bias = 15
Binary representation is: $0 \, 00000 \, 0000000001 = 2^{-14} * 2^{-10}=2^{-24}$
I've understood the binary representation part, but how does it get to those exponents of 2??
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 $+0.0000000001_2 \times 2^{-14} = 2^{-24}$.