digital and quantized signal, are one same thing?
Generally, yes, but it depends. Digital audio is a quantized signal, but class D amplifiers (which quantize in the time dimension) are not considered digital. I guess you could think of digital as complete quantization.
How the calculator decodes the digital signal?
Do you have some particular kind of digital signal in mind? Audio, video, or what?
Electrical engineering and electronics isn't my field, but I do know that there are a variety of ways of modulating digital data onto an analog carrier signal, and which ones are used depends on the application. For digital television, for example, there are 8VSB (ATSC) (used for broadcast TV in the USA and some other places), QAM (used for cable TV in the USA), DVB (used for broadcast TV in Europe), etc.
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