Japt -h
, 1110 bytes
ñÈu2pHÉñÈu2pH)¤¬x
ñÈu2pHÉñÈu2pH)¤¬x :Implicit input of array
ñ :Sort by
È :Passing each element through the following function
u :Positive modulo
2p : 2 raised to the power of
H : 32
É : Minus 1
) :End modulo
¤ :To binary string
¬ :Split
x :Reduce by addition
:Implicit output of last element