ospf area id is a 32 bit number...

just like an ip address... in other words an ospf area id of 1 can also be expressed as 0.0.0.1 on one side and  1 on the other...

network 10.1.1.0 0.0.0.255 area 0.0.0.1

and

network 10.1.1.0 0.0.0.255 area 1

these networks have the same area id... easy enough...

what is 2^32? all 1's or f's or 255's, or...

4,294,967,295

which of course is 4,294,967,296 total numbers because of the 0...

area id 0.0.1.1 = area id 257

that's a scott morris example right there... God forbid you get hit with this kind of bullshit on d-day... and that's an easy one...

why does 0.0.1.1 = 257?

because 1 in the 3rd octet is the 24th bit place holder from the left which equals 256 and 1 in the 4th octet is the 32nd bit place holder from the left which equals 1...

as you can see below...

another easy example:

area id 271

that is 256 + 15

0.0.1.15

0.0.2.15 and it starts to suck

the last four place holders = 15 as before but in the third octet we've moved up a place holder

512 256 128 64 32 16 8 4 2 1

512 + 15 = 527

get comfortable with all the powers of 2, because that ain't nice...

it gets worse...

area id 0.0.3.0 = 768 because

512 256 128 64 32 16 8 4 2 1

you have to start adding the big place holders...

area id 1024 is

1024 512 256 128 64 32 16 8 4 2 1

or 0.0.4.0

knock yourself out...