The only thing related to IP addressing you need to be able to understand in binary terms are subnet and wildcard masks. Otherwise, there's very little reason to convert an IP address to binary.
Once you understand subnetting, you'll realize that it's a lot easier than that ridiculous formula makes it seem.
For instance, if you're given 192.168.0.0/16 and you're told that you need 100 subnets, all you need to do is figure out which power of 2 gives you the number over 100. 2^7 = 128, meaning you need 7 bits to identify subnets. That means that each subnet is going to have a /23 (16+7) subnet mask (255.255.254.0).
If, on the other hand, you are given 192.168.0.0/16 and are told that you need multiple subnets with 480 hosts in them, you work backwards. 2^9 = 512, so each subnet needs 9 host bits. That means each subnet has to have a /23 (32-9) subnet mask (again, 255.255.254.0).
Learn your powers of 2 and understand what a subnet mask actually does, and subnetting is incredibly easy. No binary necessary, other than to recognize that /23 means 23 consecutive 1's followed by 9 consecutive 0's to form the subnet mask, represented in decimal as 255.255.254.0. But, there are really only 8 numbers you need to remember:
00000000 = 0
10000000 = 128
11000000 = 192
11100000 = 224
11110000 = 240
11111000 = 248
11111100 = 252
11111110 = 254
11111111 = 255
Once those become second nature, nothing else matters.