A clock has a 1ns clock period with rise and fall time as 0.05ns. The clock signal stays at exact Boolean state 1 for 0.35ns and at state 0 for 0.55ns. The memory used in the design takes 2 clock cycle time to compute a write and 1 clock cycle to compute a read operation.
What is the frequency of this clock? My attempt: $T = 1/f \Rightarrow f = 1/T = 1/1ns = 1/10^{-9}s = 10^9s = 10^{15}μs$
What is the duty cycle of this clock? My attempt: $D = t_hh/T * 100 = (0.35ns/10^{-15}μs) * 100 = 0.00035μs/10^{-15}μs = 3.5^{13}μs$
Could someone please kindly confirm whether I did this correctly or not?
The calculator sure is right about the numbers, but you didn't enter any units, right?
Regarding the frequency, you are right for this part $$T=1/f \Rightarrow f=1/T=1/1\text{ns}=1/10^{−9}\text{s}$$ Note that the last term is to be read as $$\frac{1}{10^{-9}\text{s}} = 10^9 \frac{1}{\text{s}} = 10^9 \text{Hz} = 1 \text{GHz}$$ and not as $$\frac{1}{10^{-9}}\text{s}$$
This hint usually applies to physics, and basically every time you deal with units: if the unit of the result is wrong, the result itself is wrong. If you are asked for a frequency (number of times something occurs in a given time span) and you come up with a time span, that's wrong.
The same thing applies to the second question: if you divide a time by a time, you get a dimensionless number. $$D = t_h/T \cdot 100\% = \frac{0.35 \cdot 10^{-9}\text{s}}{1 \cdot 10^{-9}\text{s}}\cdot 100\% = 35\%$$