GATE 2018 IN Q.19: solution and answer

Official answer: CSource: Official answer key, GATE 2018 IN (IIT Guwahati)

1. A flash (parallel) ADC compares the analog input with every quantisation threshold at the same time. Each threshold needs its own comparator.

2. An $n$-bit converter has $2^n$ output codes, from $(00\dots 0{)}_2$ to $(11\dots 1{)}_2$. To separate $2^n$ adjacent levels you need $2^n-1$ boundaries between them, so the converter needs $2^n-1$ comparators. A resistor ladder of $2^n$ resistors across the reference voltage produces those $2^n-1$ threshold voltages.

3. The comparator outputs form a thermometer code: every comparator whose threshold is below the input reads 1, and every one above it reads 0. A $(2^n-1)$-input priority encoder converts this into the $n$-bit binary output.

4. For $n=8$: $$N_{\text{comp}}=2^n-1=2^8-1=256-1=255$$

5. The answer is option (C), 255.