Here's how to calculate it:

* Frequency (f) and Period (T) Relationship: Frequency and period are inversely proportional. This means:

* T = 1/f

* Frequency in Hertz (Hz): 1 GHz = 1,000,000,000 Hz (one billion Hertz)

* Calculation:

* T = 1 / 1,000,000,000 Hz

* T = 0.000000001 seconds

* T = 1 nanosecond (ns)

Therefore, a clock with a frequency of 1 GHz has a period of 1 nanosecond.