digital electronics

ISB123

Joined May 21, 2014
1,238
if 1ms=0.001 than 10ms=0.01 .
I just know the conversion in my head didn't really do anything mathematical.
You just need to know that 1s is 1000ms.
 

Veracohr

Joined Jan 3, 2011
694
When dividing by powers of 10 move the decimal one place to the left for every 0.

So 1/10 is 0.1
1/100 is 0.01
1/1000 is 0.001

Etc.
 

Thread Starter

james7701

Joined Jan 5, 2016
37
if 1ms=0.001 than 10ms=0.01 .
I just know the conversion in my head didn't really do anything mathematical.
You just need to know that 1s is 1000ms.
so ,when it's stated that the frequency of a pulse waveform is the reciprocal of the period, that means that the time (in some form of seconds)must be converted to get the correct frequency?
 

WBahn

Joined Mar 31, 2012
24,974
so, from the last zero u count 3 times to the right <--- to get 0.01? or do u have a chart to show the conversions?
Let's take it in two steps.

First, do you know that 1 second is the same as 1000 milliseconds?

If not, then you first need to get comfortable with unit prefixes in the SI system.

http://physics.nist.gov/cuu/Units/prefixes.html

https://en.wikipedia.org/wiki/Metric_prefix

For the most part, the only ones you really need to be fluent with are the powers of 10^3, which are

10^12 pico
10^-9 nano
10^-6 micro
10^-3 milli
10^3 kilo
10^6 mega
10^9 giga

You also want to be comfortable with 10^-2, which is centi, because of the widespread use of "centimeter", though it isn't used for much else these days (at least not directly).

Once you have that down, the second part can be handle by just remember that if you multiply anything by 1 then you don't change it's value and that if you divide 'a' by 'b' and if 'a' and 'b' are equal then the result is 1.

So if

\(
f \; = \; \frac{1}{T}
\)

The T isn't just some time, it is the amount of time for one cycle of the waveform. So if one cycle takes 10 ms, T is not equal to 10 ms, it is equal to 10 ms-per-cycle, or 10 ms/cycle.

\(
f \; = \; \frac{1}{T} \; = \; \frac{1}{10 \frac{ms}{cycle}} \; = \; \0.1 \, \frac{cycle}{ms}
\)

Now, since 1 s is equal to 1000 ms, if we divide one by the other we just have 1, which we can multiply our equation with and not change the value.

\(
f \; = \; \( \0.1 \, \frac{cycle}{\strike{ms}} \) \( \frac{1000 \, \strike{ms}}{1 \, s}\) = \; 100 \, \frac{cycle}{s}
\)

Finally,

\(
1 \, Hz \; = \; 1 \, \frac{cycle}{s}
\)

So we can do this again (multiply our equation by the ratio of two things that are equal) to get

\(
f \; = \; \( 100 \, \frac{cycle}{s} \) \( \frac{1 \, Hz}{1 \, \frac{cycle}{s}} \) \; = \; \( 100 \, \frac{\strike{cycle}}{\strike{s}} \) \( 1 \, \frac{Hz \, \strike{s}}{\strike{cycle}} \) \; = \; 100 \, Hz
\)
 

AnalogKid

Joined Aug 1, 2013
8,226
do u have a chart to show the conversions?
The International System of Units (abbreviated SI) is the system that describes quantities and numerical relationships in science and engineering. These are the guys that define that 1/1000 of a second is called a millisecond, and is abbreviated ms, and one billion gigabytes is called an Exabyte, and is abbreviated EB. It started out as the metric system, and has expanded to cover all weights, measures, quantities, etc.

https://en.wikipedia.org/wiki/International_System_of_Units

ak
 

Veracohr

Joined Jan 3, 2011
694
so ,when it's stated that the frequency of a pulse waveform is the reciprocal of the period, that means that the time (in some form of seconds)must be converted to get the correct frequency?
Perhaps you should look at the definition of frequency: the number of cycles per second. 100Hz = 100 cycles/second. The period (T) is the time one cycle takes, so divide 1 second by 100 cycles (1/100) = .01 seconds per cycle.

1/100 = .01
1/.01 = 100

So the period T=1/f, and the frequency f=1/T.
 
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