00:01
Okay, so we want to find how many messages can be transmitted in n microsecond.
00:05
So what we have here is one signal requires one microsecond.
00:12
So if you imagine, let's say, a, n being here, then this signal, you have to start off at a .n minus one, or time, n minus one, and in one microsecond, you're able to receive the message at n.
00:25
But two signals require you to start at a .n.
00:30
Minus two because it takes two microseconds.
00:32
So one signal here and another signal comes here.
00:36
So then the number of signals at a sub -n is going to be a -sub -1 plus by two times by a -n -min -2, because two signals from here and one signal from there.
00:50
Now, in zero microseconds, exactly one message can be sent, the empty message.
00:56
So a 0 is equal to 1.
01:00
Then in one microsecond only one signal can also be also one signal can be sent because of the a n minus 1.
01:09
So the characteristic equation then is well if i move this this way a sub n minus by a sub n minus 1 or minus by 2 a sub n minus 2 is equal to 0.
01:24
Then we let a sub n be equal to, let's say, r squared.
01:30
So you have r squared minus by r minus by two is equal to zero.
01:38
So then factorizing, you have r minus two times like r plus one is equal to zero...
