There are several advantages of using digital signal over their analog counterpart which prompted the shift to digital decades ago:

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1) Noise immunity for communication

Digital signal have more 'noise immunity' for t=long range communication than thei analog counterparts mainly because of the following:

· Repeaters: Since, digital signals consists of discrete information( which is usually modulated into the phase of an analog signal as in Phase-shift keying and the digital signal of 1/0 is not directly transmitted unlike what some people think) , if it gets degraded over time, one can use digital repeaters to demodulate the signal, clean it by assigning to the nearest voltage level and then retransmitting it. In analog repeaters, the best you can do is amplify the signal which boosts the existing noise as well as the signal.



· Error Correction Coding: Even after going through several repeaters if there is some error, those can be corrected by built in 'smart' redundancies in the signal called error correcting code. Because of these redundancies, even if there is some error in the signal, it can be corrected at the receiver. (All this is possible due to the famous shannon's theorem: Noisy-channel coding theorem )



2) Data storage

In general data needs to be discretized in order to store them. For some kind of data you might be able to store them fully in analog (like vinyl records store sound in continuous time and value) and some other times you have to discretize one dimension(like video is discretized in temporal dimension but not in the spatial dimension in old films: one analog picture per time frame). But even if you are able to store it analog it is usually better to store them digitally because stored signals degrade over time and the error-correcting codes discussed in part (1) can help mitigate that: thus producing error free storage of signals. Also, digital signals can be compressed by utilizing the signal's inherent redundancy and thus reducing storage requirements.

3) Data processing

Although 1-dimensional analog signals can be filtered in analog domain, for multidimensional data(like images) you need to do it in digital domain. Also more complicated computation on signals cannot be done easily(or sometimes not at all) in the analog domain.

Even if you could process signals in the analog domain, it is better to do it in digital domain, because analog filtering adds some noise and it is very expensive to produce analog components with identical characteristics: so each analog filter will behave slightly differently introducing noise. It is much much cheaper to process them digitally with near identical or better performance than analog but with some additional processing time (There is no free lunch).

By the way you phrase your question, I’m not sure if you understand what you are asking. There is, really, no such thing as a “digital signal”, as far as we know. That might sound strange, since many of us study “digital signal processing”. There are only analog signals. We use techniques to try to take a snapshot of these analog signals, and we store these snapshots, for example, in analog wells of charge, where higher charges are designated as ones and lower charges are designated as zeros. Really though, they are poor copies of the analog signals.

So really digital signal processing is really analog signal processing.

There is, really, no such thing as a digital signal.

See here is a good summary of advantages of converting analog signals to digital before you process them.

Pros:

1. More immune to the effects of Noise. As they are binary in nature, significant amount of noise is needed to distort the values from 1 to 0 and vice versa.

2. Modern devices implement circuits that work on digital signals, and hence working with digital signals provides a uniform platform and environment.

3. Use of digital signals also permits storage of data for future processing/reference.

Depending on the use case, one can come up with many more advantages of the use of digital signals. But, I think these are most common pros of using digital signals.

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Source: Quora