# what is the resolution?

Discussion in 'Electronics Homework Help' started by charmcaster.engg, Jan 20, 2015.

1. ### charmcaster.engg

79
1
Mar 20, 2014
The resolution of a 0–5 V 6-bit digital-to-analog converter (DAC) is:
I have done 5/64=0.078.but answer is 1.56%.?

2. ### Gryd3

4,098
875
Jun 25, 2014
6-bits will provide you with 64 steps from 0v to 5v. (Each step is 1.56% of the total range)
Each step will be 78mV like you have calculated.
This is my understanding of resolution... however, the 1.56% is a different representation.
If this question did not include the "0-5 V" description, I would have given the percentage. Looking at the question as you presented it though, I would have done exactly what you have.
In a question like this, there may have been an expected output. Did the question ask for a percentage or voltage? Does the instructor have a preference? Where did you get your answer?

3. ### charmcaster.engg

79
1
Mar 20, 2014
I don't have any other info. They may have given wrong answer.

4. ### Gryd3

4,098
875
Jun 25, 2014
Who is 'they' ?

5. ### charmcaster.engg

79
1
Mar 20, 2014
I am solving these question from one of the website.

6. ### Gryd3

4,098
875
Jun 25, 2014
Well, do you understand where the 1.56% came from?
Both answers are acceptable depending on the circumstance.

7. ### davennModerator

13,618
1,882
Sep 5, 2009
what www site ?

79
1
Mar 20, 2014

9. ### Gryd3

4,098
875
Jun 25, 2014
If you can share the website you are using, it would be appreciated..
Anyway, here are some numbers for you:

6-bits provide 64 possible combinations. ( 0 - 63 )
Now.. even though there are 64 combinations, there are only 63 steps.
So, if you take the reciprocal which is 1 / 63, you find that each step is 1.59% of the whole.
Using the same number, you find that each step of a 5V DAC is 5V / 63 = 0.079V

So at this time you can build a table:
000000 = 0% (0v)
000001 = 1.59% (0.079v)
000010 = 3.18% (0.158v)
000011 = 4.76% (0.238v)
000100 = 6.35% (0.317v)
...
111101 = 96.82% (4.84v)
111110 = 98.41% (4.92v)
111111 = 100% (5v)

Or simply multiply the binary value by the resolution to determine the answer:
So 011000 must be?

10. ### charmcaster.engg

79
1
Mar 20, 2014
38.16% .Thanks!