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Brainfuck, 157 bytes
-[+[+<]>>+]<+++.[->+>+<<]>>++>>,[>-[<->-----]+<+++[-<+<<.>>>>-<]>[-<<-[->+<]<<<[-]>>>>[-<+<<<+>>>>]<<.>>+<[>-]>[-<+<<.>>>>]<<>>]<,]<<<<[>.>.<<[-]]>>>+[-<.>]+
Reads an integer in binary on stdin, and outputs the nested list on stdin. Requires 0 to be input as the empty stri...