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#Mathematica, 60 bytes
Tr[Last@*Accumulate/@(#[[1]]2^(Range@Tr[1^#]-1)&/@Split@#)]&
#Mathematica, 6160 bytes
Tr[Last@*Accumulate/@(#[[1]]2^Range[0,Tr[1^#]#[[1]]2^(Range@Tr[1^#]-1]&1)&/@Split@#)]&
#Mathematica, 61 bytes
Tr[Last@*Accumulate/@(#[[1]]2^Range[0,Tr[1^#]-1]&/@Split@#)]&
