How to convert binary data with primitive data types

Have you checked for endianness? Erlang assumes big-endian-arranged bytes when extracting floats the way you are doing it.

Demo:

bin = <<:math.pi()::float-32>> <> <<0, 0, 0>>
<<64, 73, 15, 219, 0, 0, 0>>

<<x::float-32, rest::binary>> = bin
<<64, 73, 15, 219, 0, 0, 0>>

x
3.1415927410125732

<<x::big-float-32, rest::binary>> = bin
<<64, 73, 15, 219, 0, 0, 0>>

x
3.1415927410125732

<<x::little-float-32, rest::binary>> = bin
<<64, 73, 15, 219, 0, 0, 0>>

x
-4.03314608963584e16

As you can see, by default big endian is used. So if your values are little-endian-arranged, you have to specify that explicitly.

In your example, try changing float-size(32) to little-float-size(32) and see if it works.