Final answer:
To design a circuit that provides a clock with a cycle time of 50 ns from an 80MHz clock generator, one needs to use a frequency divider that divides the frequency by 4, giving a resultant frequency of 20MHz.
Step-by-step explanation:
The question involves designing a circuit that will provide a clock signal with a cycle time of 50 nanoseconds (ns), given an initial clock generator frequency of 80MHz.
To achieve a 50 ns cycle time, you need a clock frequency of 20MHz because the cycle time (T) is the reciprocal of the frequency (f), or T = 1/f. Since 1/(20MHz) is 50 ns, we need to divide the 80MHz clock by a factor of 4. This can be accomplished using a frequency divider, which is a digital circuit that takes an input clock frequency and outputs a clock frequency that is a lower division of the input.
A simple way to create a frequency divider by 4 is to use a counter that counts two bits (since 22 = 4). Each time the counter goes through its full range, it will output a single pulse, effectively dividing the input clock frequency by 4. Using such a frequency divider, you can convert the 80MHz input to the required 20MHz output, which corresponds to the 50 ns cycle time needed for the clock.