If an analog signal is converted by an analog to digital con

If an analog signal is converted by an analog to digital converter to a binary representation and then back to an analog voltage using a DAC, will the original analog input voltage be the same as the reulting analog ouput voltage?

The answer is no but why?

Solution

Answer is NO.

If the analog signal given and we have taken reference value as 10 volts and in the analog to digital converter for 8 bit we have to take resolution that is 10/ (2^8-1) = 0.03921568633 but we have taken as approximation as 0. 039 thus resolution changes the output value and we can apply least value as 0. 039 mv only in the approximation.... If we have less than the resolution or just greater than resolution like 0.040 mv it only gives the bit output as high because 0.040>0.039 but remaining 0. 001 ( 0.040-0.039) is not considered in the digital output.....so if the digital output comes and if we convert it into analog it gives approximation value only but not the exact value as given input. The DAC output is in terms of resolution only.