Nope. They don't match.
Decimal IP notation is just an easier way to represent a binary IP. You can change a decimal IP to a binary IP and back, but there is no other way for them to magically convert to other numbers.
To convert a decimal IP to binary, we split up the four octets, and convert each decimal number to its binary representation.
So for your IP, 184.108.40.206:
- 83 → 01010011
- 226 → 11100010
- 175 → 10101111
- 75 → 01001011
Put them all back together, and your binary IP is 01010011111000101010111101001011. Notice that's a totally different binary number than what you've got. In particular, it's much shorter.
(And it's not contained anywhere within your binary number.)
To convert from binary to decimal, we do the opposite (which you started): break it into 8-bit chunks and convert each one to its decimal representation.
If we try to convert your binary number to a decimal IP, we get this:
- 00110111 → 55
- 00110100 → 52
- 01110101 → 117
- 00110000 → 48
- 01000100 → 68
- 01101011 → 107
- 01101010 → 106
- 00110010 → 50
- 01010001 → 81
If we put those decimal numbers together like an IP, it would be 220.127.116.11.18.104.22.168.81. That's clearly not an IP. It could be two IPs, smushed together, plus an extra octet, but that's not something I'd expect to encounter in networking.
Perhaps if you tell us where that string came from, somebody can give you a better idea what it means