Absolute Coder Resolution in Degrees: Calculating 360/25

In summary, Jedi found an error in a popular math book that resulted in 25 being used instead of 2^5.
  • #1
Femme_physics
Gold Member
2,550
1
Resolution in "degrees"?

Homework Statement


In the following scheme we see the channels spreadout of an absolute coder with 5 bits that works on a regular binary code. What's his resolution in degrees?

http://img705.imageshack.us/img705/475/01234v.jpg [Broken]



The Attempt at a Solution



I don't ever recall measuring resolution in degrees.

However, I see the solution in the solution manual is just this: 360/25 = 11.25 degrees / bit

My question is simple...where did he take the 25 from? I see the numbers range from 0 till 31... excuse the bad quality.
 
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  • #3
Thanks, Jedi, I'll ask my teacher on class Friday (it's his solution manual)
 
  • #4
Femme_physics said:
Thanks, Jedi, I'll ask my teacher on class Friday (it's his solution manual)

I saw an error like this in a popular math book the guy meant to say 2^5 but the copy-editor put in 25 and this may be the real source of the error you discovered.
 
  • #5
If you look at the picture, the values run from 0...31, which is 2^5

Astronomers deal with resolution not so much in degrees, but in seconds of arc.

3600 arc seconds = 1 degree.

For resolutions in degrees, this suggests regulation of something like a stepper motor, which turns a fixed portion of an arc every time it is actuated.
 
  • #6
The question didn't specify such fancy data :) But thanks for the input.

I saw an error like this in a popular math book the guy meant to say 2^5 but the copy-editor put in 25 and this may be the real source of the error you discovered.

It won't be the first time I approach teachers with errors, nor the first time I'll be submitting errors to solution manuals :-) Just ask username "I Like Serena", we used to do it a lot in mechanics! So, I trust the users of PF :)
 
  • #7
jedishrfu said:
I saw an error like this in a popular math book the guy meant to say 2^5 but the copy-editor put in 25 and this may be the real source of the error you discovered.

Nice observation.
Note that 360/25=14.4, while 360/2^5=11.25.

Oh, and happy birthday Fp!
 

1. What is resolution in degrees?

Resolution in degrees refers to the smallest angle between two points that can be distinguished by a measuring instrument or system.

2. How is resolution in degrees calculated?

Resolution in degrees is typically calculated by dividing the total range of angles by the number of divisions on the measuring scale or system.

3. What factors affect resolution in degrees?

The main factors that can affect resolution in degrees include the precision and accuracy of the measuring instrument or system, as well as external factors such as temperature and environmental conditions.

4. Can resolution in degrees be improved?

Yes, resolution in degrees can be improved by using more precise measuring instruments or systems, as well as by reducing external factors that can affect the measurement.

5. Is resolution in degrees the same as precision?

No, resolution in degrees and precision are two different concepts. Resolution refers to the smallest angle that can be measured, while precision refers to the consistency and reproducibility of the measurements.

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