Calculate number of bits in analogue to digital converter

Question

The output of a strain gauge transducer consists of a full scale value of 5Volt. The value of the output is exact to in + 10mV and is to be digitized for storage within a PC. Calculate the number of bits needed into the analogue-to-digital converter.

Answer 1

The absolute value of error is + 10mV. This must correspond to + ½ a quantization level.

That's why 10mV = ½ V_Q

Therefore V_Q = 2 x 10 mV = 20mV

So, if

V_Q = V_FS/(L-1) in that case L - 1 = V_FS/ V_Q

L = V_FS/ V_Q + 1

Numbers of levels are as follows:

L = (5V/20mV) + 1 = (5/0.02) +1 = (500/2) + 1

= 251

N = log₂251 = 7.9716

We should the next highest interger value therefore:

Number of bts needed are: N = 8