Converting IPV4 address into Binary
I am going to answer this question in two parts:
First,
Without reaching into the depths of communication, I want to mention that the data that humans do understand(such as this answer which I am typing) is classified under Layer 7 of the TCP/IP stack. This data gets converted into analog signals that travel over the wire, and any hosts connected to these wires translate these analog signals to electric signals. Electric signals have two states, 0 and 1, which we humans call binary format.
So any data on the wire would essentially be looked upon as a sequence of bits and bytes.

The IP address that you mention, is a component of the IP Protocol, and this protocol is used to carry packets end to end between two hosts on a network. So, the data would be added as a payload on top of an IP packet which contains a IP header. Any devices in between these two hosts which operate on Layer-3 of the TCP/IP stack(the network layer!) would use this header to process the packet. Similarly the end hosts would use this header to determine if the packet indeed was sent to them. 
The IP protocol specifies the syntax and semantics of the IP Packet header, and as you might notice the size of the fields are fixed. Now any machine which is looking at a sequence of bits coming in (with the knowledge that it is receiving the IP header) can just read as many bytes as it wants to extract every field of the header. For example, given that the system knows where the IP header starts, the system could read the first 4 bits and understand that it would just read the version of IP packet.  

Second,
The conversion that you mentioned, between binary and dotted decimal, is purely for representing data in human readable format(as the other answer mentions). Tools like Wireshark do this to show details of a packet(the internals of this are fascinating). So, you can choose whichever method to convert one form to the other, but the machines don't really need to do this at the level of the TCP/IP stack where it really matters.  The system doesn't really see it as a dotted decimal construct, but a data structure which consists of four 8 byte fields, (or two 16). 

Hope this helps !