The number of comparators required for implementing an 8-bit flash analog-to-digital converter is

Flash ADC Comparator Calculation for 8-Bit Resolution

A flash Analog-to-Digital Converter (ADC) is known for its high speed because it converts the analog input voltage to a digital output in a single clock cycle. It achieves this by simultaneously comparing the input voltage with a series of reference voltages.

Understanding Flash ADC Comparators

For an ADC with a resolution of N bits, there are $2^N$ possible digital output codes. These codes represent discrete voltage levels. A flash ADC uses comparators to determine which range the input analog voltage falls into.

Each comparator checks if the input voltage is greater than or less than a specific reference voltage. To distinguish between all the possible output levels, a specific number of comparators are required.

Calculating the Number of Comparators

The relationship between the number of bits (N) and the number of comparators in a flash ADC is given by the formula:

Number of Comparators = $2^N-1$

In this specific question, the resolution is given as 8 bits. Therefore, N = 8.

Let's substitute N = 8 into the formula:

- Calculate $2^N$: $2^8=2\times 2\times 2\times 2\times 2\times 2\times 2\times 2=256$.
- Subtract 1: $256-1=255$.

Thus, an 8-bit flash ADC requires 255 comparators. These comparators generate a "thermometer code" output, which is then typically converted into a binary code by a digital encoder.

The number of reference voltages needed is $2^N$, which is 256 in this case. Each comparator compares the input voltage against one of these reference voltages (except possibly the highest and lowest).

Final Answer Derivation

Based on the calculation, the number of comparators needed for an 8-bit flash ADC is 255.