GATE 2026 IN Q.35: solution and answer

GATE 2026 · INQ.35 · 1 mark · NAT

The minimum number of comparators required in a 6-bit flash analog-to-digital converter is ________. (answer in integer)

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Answer and solution

ANSWER

The minimum number of comparators in a 6-bit flash ADC is $2^{6} - 1 = 63$ .

Official answer: 63Source: Official answer key, GATE 2026 IN (IIT Guwahati)

A flash (parallel) ADC with $n$ output bits divides the full-scale input range into $2^{n}$ quantisation levels. Between $2^{n}$ adjacent levels there are $2^{n} - 1$ decision thresholds.
Each threshold needs its own comparator. A resistor ladder sets the reference voltage for each comparator. All the comparators switch at once and produce a thermometer code, and a priority encoder turns that code into the $n$ -bit binary output.
So the number of comparators in an $n$ -bit flash ADC is $2^{n} - 1$ .
For $n = 6$ : $2^{6} - 1 = 64 - 1 = 63$
A 6-bit flash ADC needs at least 63 comparators.

KEY IDEA

An $n$ -bit flash ADC compares the input against every decision threshold at once, with one comparator per threshold. $2^{n}$ levels have $2^{n} - 1$ thresholds between them, so it needs $2^{n} - 1$ comparators. This count doubles with every added bit, which is why flash converters are fast but expensive at high resolution.

WATCH OUT FOR

Answering $2^{6} = 64$ (counting levels instead of the thresholds between them), or answering 6 (mixing up the flash ADC with a successive-approximation ADC, which uses a single comparator for $n$ clock cycles). The resistor ladder has $2^{n}$ resistors, but it needs only $2^{n} - 1$ comparators.

From the GATE 2026 IN paper. Every question of this paper · Download the full paper · All 18 ADC & DAC questions, with notes

GATE 2026 IN Q.35: solution and answer

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