Number of bits and resolution my answer VS my teacher's

[Femme_physics]

Homework Statement

A load cell converts weight to voltage. It's known that the transmission of a certain measurement system is 5 mV/kgf


In a computerized control system, it is necessary to translate the analog signal, which the transducer sends off, to a digital signal through an A/D converter.

In a certain weight system, it is necessarily to measure weight in the range of 0-200 kgf, whereas the needed accuracy of the measurement is 0.5 kgf

The A/D converter which is in the conversion system, is supplied by a 5V DC (Direct Current) voltage.

1) Pick the appropriate A/D converter for this measurement system (what's the required "data bits"?)

The Attempt at a Solution

What bothers me is that I got n = 10 and he got n = 11. What gives?

My solution:

http://img827.imageshack.us/img827/7513/myann.jpg

My teacher solution: (Don't mind the Hebrew words)

http://img703.imageshack.us/img703/5646/teacherans.jpg

 

[NascentOxygen]

Hi FP. It is just an arithmetic error (on your part) I think.

0.0025 ≤ 5/(2ⁿ - 1)

2ⁿ - 1 ≥ 2 x 10³

if n=10, LHS = 1023
if n=11, LHS = ...

 

[I like Serena]

How did you find your n=9.64?

 

[rude man]

Has nothing to do with the 5V a/d converter reference. We are interested in resolving 0.5kg/200 kg. If the LSB is 0.25kg and the actual weight is say 10.25 kg then we could get a reading of either 10.00 or 10.50 which is at the limit of requirement, so you should resolve to 0.125 kg which implies 200/.125 = 1600 LSB's or n = 11.

 

[Femme_physics]

Nascent is right, I just reset my calculator and recalculated. It is indeed n =11 :-) Thank you for the replies.

 

[jedishrfu]

Nascent is right, I just reset my calculator and recalculated. It is indeed n =11 :-) Thank you for the replies.

Bad calculator! Bad! Switch to a slide-rule. :-)