Recently we had a project were area 1000 was picked as an area for OSPF with some non-cisco devices. The people who managed the non-cisco devices scoffed because they were only used to and might have only been able to do ospf areas with in the octects (eg. area 0 = 0.0.0.0, area 1 = 0.0.0.1, etc.). For simplicity we just chagned to a different area under 255, however I was curious what if we couldn't for some reason. What would the correct area to give them be ? My thought would be 0.0.3.232 because 1000 in binary is 11 1110 1000

11 = 3 1110 1000 = 232

Would this have been correct ? And I'm not just curious about the binary math, I'm also curious about the w.x.y.z areas translating directly into number like that for the ospf areas.

He's talking about an area ID, not a wildcard mask.

Yes, the number 1000 expressed in dotted-decimal is 0.0.3.232. But whether you specify an area ID in decimal or dotted-decimal (IPv4 notation) is irrelevant: it's a simple 32-bit number either way.