Iam trying to solve this so plug in a random value in for V, and show me the steps.
You question is not clear. However, let me attempt to have a go at answering it based on what I think you are doing.
Suppose you have a voltage, that varies from 0v up to a maximum of 10V. This voltage may be the output that comes from some circuit. We call the maximum voltage 10V.
The 0-10 V is an example of an analogue voltage, but in order to get it into the computer It's going to have to be converted to a digital one and we can do this using a analogue to digital converter or A/D for short.
The A/D converter effectively divides the entire voltage range (0-10V) into a number of equal steps. The number of steps this voltage is divided is determined by your n value.
If n = 2, then the number of steps the voltage will be divided by will be:
2^n or 2^2 or (2 x 2) = 4.
This means the output from the 2 bit A/D will be the 0-10V divided into 4 equal steps starting at zero
giving each step an interval of 10V/4 = 2.5V The A/D gives this to the computer as:
00 (2.5V)
01 (5V)
10 (7.5V)
11 (10V)
The LSB you are trying to calculate is the voltage required to change the digital output state (also known as the Least significant bit value or resolution) In this case 2.5V.
If my 0-10V output came from a temperature amplifier combination calibrated to correspond to 0-100 Deg C then the best I could hope to detect is 25 degree intervals.
If I want to get better resolution , say detect a change in every degree then I need to use a A/D converter with more bit resolution, that is increase n. Typically, A/d come with 8 bits (n=8) or 12 bits (n-12)
An 8-bit A/D will divide the 0-10V voltage range into 2^8 equals steps. 2^8 = 256
so each step will be 10/256V = 0.039V . Each time the voltage increased or decreased by 0.039V it would change the value (1 or 0) of the least significant bit of the A/D.
00000000 = 0V
00000001 = 0.039V
00000010 = 0.078V
00000011 = .117 V
..
..
11111111 = 10V
By using a greater value for n (8- bit A/D) wee increase the resolution of our measurement. Since 0-10V from the sensor amplifier combination maps to 0-100 Deg C then each 0.039Change corresponds to 0.39 Deg C This means that you can detect less than a one degree change in temperature. However, if the 0-10V is the sensor amplifier combination that maps to 0-1000 Deg C then the temperature resolution is now 3.9 deg C.
If we want better resolution we need to go to a 12-Bit system which divides the voltage range by: 2^12 = 4096.
Hi:
It's Not V in voltage the it mean Vfsr is full scale range for a analog to digital converter
however if you have the LSB value and the Vfsr Value than this how you find the 2^n value
LSB = Vfsr / 2^n - original equation
1/ LSB * LSB = Vfsr / (2^n) * (1 /LSB) - timing both sides of the equation with 1/LSB to move LSB from side of the equation to the other side of it
1 = Vfsr /(( 2^n) (LSB)) - Multiplication
2^n * 1 = Vfsr /(( 2^n) (LSB)) * 2^n - timing both sides of the equation with 2^n to remove 1/(2^n) from side of the equation to the other side of it
2^n = Vfsr / LSB - Multiplication
to slove for n use the log Power rule to slove for that
log(2^n) = log (Vfsr / LSB ) taking the logarithm of both sides of the equation to remove the power from the equation
n log (2) = log (Vfsr / LSB ) - power rule of logarithms
1/ log (2) *n log (2) = log (Vfsr / LSB ) * 1/ log(2) timing both sides of the equation with 1 / log( 2) to remove 1/ log(2) from side of the equation to the other side of it
n = log( Vfsr / LSB ) / log (2) - Multiplication
Here a website:
http://www.ti.com/lit/an/sbaa046/sbaa046...
I hope this helps .
This simply says that the least significant bit represents a fraction of the full scale voltage, the fraction being a function of the number of bits n. So if the full scale voltage Vfsr = 5 and you have an 8 bit system, then you can resolve 5/256 = 0.01953125V. Typically Vfsr is the reference voltage for the DAC.
I am sorry, you question doesnt seem very clear to me. What is the unknown quantity here ?? do you have the value of n.
2^n can be calculated using log. An easier way to calculate this is by using a scientific calculator. If you dont have a scientific calculator, you can find one online.
Why don't you write a simple program in any computer language to let the computer calculate for you.
A simple DO-loop instruction can compute it.
Iam solving for the equation LSB = Vfsr/2^n for a digital circuit?
Iam trying to solve this so plug in a random value in for V, and show me the steps.
