In an ideal analog-to-digital conversion chain, which order of blocks yields a digital output?

• A. A Sampler, Quantizer, Encoder, yielding digital output
• B. B Encoder, Sampler, Quantizer, yielding digital output
• C. C Quantizer, Encoder, Sampler, yielding digital output
• D. D Sampler, Quantizer, Encoder, yielding digital output

Answer: (D)

The main idea is converting a real-valued analog signal into a digital stream step by step: first turn the continuous-time signal into samples, then map those sample values to a finite set of levels, and finally represent each quantized level with bits. So you start with a sampler to create discrete-time samples from the analog signal. Next, a quantizer converts each sample’s amplitude to a nearest level in a finite alphabet. Finally, an encoder translates that discrete level into a binary word, producing the digital output. If you tried to encode before quantizing, you’d be asking to produce a digital word from values that aren’t yet restricted to a finite set. If you sampled after encoding, you’d be trying to digitize something that hasn’t been quantized yet. If you quantize before sampling, you’d be quantizing without having discrete-time instants to represent, which isn’t how an ADC is implemented. Therefore the only order that yields a proper digital output is Sampler, Quantizer, Encoder.