Absolute Coder Resolution in Degrees: Calculating 360/25

[Femme_physics]

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

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.

 

[jedishrfu]

I think the book is wrong and that it should be 32 unless there's some bits used for other purposes like error detection or correction:

This may help by way of example:

http://mechatronics.mech.northwestern.edu/design_ref/sensors/encoders.html

Is there anything about gray codes in your book?

http://en.wikipedia.org/wiki/Gray_code

while I couldn't find a connection to the 25 it seemed that gray codes might be relevant here.

 

[Femme_physics]

Thanks, Jedi, I'll ask my teacher on class Friday (it's his solution manual)

 

[jedishrfu]

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.

 

[SteamKing]

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.

 

[Femme_physics]

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 :)

 

[I like Serena]

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!