# Clock Frequency and Duty Cycle

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.

1. What is the frequency of this clock? My attempt: $T = 1/f \Rightarrow f = 1/T = 1/1ns = 1/10^{-9}s = 10^9s = 10^{15}μs$

2. 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?

• Your units are off. $1/10^{-9}s \neq 10^9s$, and you seem to be using $f$ instead of $T$ for the duty cycle. – Jasper Feb 17 '15 at 23:47
• Sorry, how is 1/10^-9s != 10^9s? I've retyped it in my calculator multiple times, and that seems to be the case... And presuming that the answer to part 1 is correct, T would then equal 10^15 instead of the negative I added in, right? – user215717 Feb 17 '15 at 23:55
• The units are off indeed. Frequency is measured in Hz, not is seconds. 1 ns period means 1 GHz frequency. – user58697 Feb 18 '15 at 0:42
• Okay, so the answer to number 1 is just 1GHz. Taking that, I would have for #2: D = (0.00035μs/0.001μs) * 100 = 35μs. Look better? – user215717 Feb 18 '15 at 0:49

## 1 Answer

I've retyped it in my calculator multiple times, and that seems to be the case.

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. $$D = t_h/T \cdot 100\% = \frac{0.35 \cdot 10^{-9}\text{s}}{1 \cdot 10^{-9}\text{s}}\cdot 100\% = 35\%$$