I know the answer to this question. What's an easy way to get the answer?

Question

Which of the following subnets is invalid? (Choose all that apply.)
a.255.224.0.0
b.255.242.255.0
c.255.255.255.253
d.255.255.127.0
e.255.255.255.192

The answers are B and C, but why are those correct? Please explain to me, that is NOT writing it out in 1's and 0's. There has to be another EASIER way!

Answer 1

The first answerer is right, in that all the 1's have to be contiguous, which explains "B", but "C" is also invalid because that would leave only two client addresses available, both of which would be taken up by the network address (x.x.x.0) and the broadcast address (x.x.x.255).

Answer 2

I think that this is about subnet masks. A valid subnet mask must have all of it's one bits be contiguous. In other words, there will be no zero bits between one bits.

Since each byte only has 8 bits, there are then only 9 legit values for a byte that has the contiguous one bits property. They are:

0
128
192 (128+64)
224 (128+64+32)
240 (128+64+32+16)
248 (... + 8)
252 (... + 4)
254 (... + 2)
255 (... + 1)

You can memorize those if you don't wanna deal with binary.