Japt, 9 bytes
ÆMgX ¤Ã¬Í
##Explanation: ÆMgX ¤Ã¬Í Æ Ã | Iterate X through the range [0...Input] MgX | Xth Fibonacci number ¤ | Binary ¬ | Join into a string Í | Convert into a base-2 number
Explanation:
ÆMgX ¤Ã¬Í
Æ Ã | Iterate X through the range [0...Input]
MgX | Xth Fibonacci number
¤ | Binary
¬ | Join into a string
Í | Convert into a base-2 number