Let's try to draw the waveform of the output that we will get. From the waveform, we can easily determine the frequency, and might also get the formula.
I am assuming that it starts with 0.
Then the signal goes through 5 inverter gates, each having a delay of 100 psec. The signal "0" is inverted to "1" after passing through the first NOT gate, then becomes "0" after the second gate, and so on. After passing through all the five gates the signal becomes "1". And had a delay of 5 x 100 psec = 500 psec. (Since, each gate takes 100 psec, and there are 5 gates).
Now in the waveform, the signal goes HIGH to level "1" after 500 psec.
Then this "1" again goes to those 5 inverter gates and becomes "0" after 500 psec. So, the waveform gets to the LOW level after being at HIGH for 500 psec.
This cycle keeps repeating, and gives us a square wave, like this:
The time period of a wave is the time of each cycle. Which in this case = 500 psec (during HIGH) + 500 psec (during LOW).
Giving 1000 psec.
And the frequency of any wave is given as 1 over time period
f = 1/T = 1/(1000 psec)
This gives the answer 1 GHz.
Some units:
$1 pico second = 10^{-12} second$
$1 GHz = 10^9 Hz$
Now, we can generalize this as the formula: (1/(2*n*t))
where, n = number of NOT gates, and t is the time delay of each gate.
Note one thing very important, if the number of gates was even, then we won't get any square wave. If the output was "1", it will always remain "1", and if it was "0" it will always remain at "0".
It's always better not to memorize any formula and trying to come up with one by yourself.
