The first time we saw a voltage divider in class was in the illustration of a flash adc. the purpose of a flash adc is to use a resistor ladder, a multiple element resistor divider, to generate multiple reference voltages. an input signal is compared to all the different reference voltages. for each resistor on the ladder that the input signal exceeds, the output value increases by 1. so that the larger the value, the higher the associated digital number. in terms of vref and r what voltage would give a binary output of 011?

where:

is the resistor where you want to know the voltage

N : the number of resistors

the sum of all resistors in the branch

Explanation:

As you know, Flash ADC are made with a ladder of resistors this resistors are usually the same value, that means that the voltage drop in each resistor is the same, (in real life the exact value is different due to the resistors have a tolerance and differs their value one each other), to analyze this we have.

the current that flows through is

if the R are the same...

the voltage drop across the last resistor is... taking into account that the first resistor is the one attached to the supply voltage.

as I said before the value of the resistors are the same so...

because of the voltage drop is the same in each resistor, we can say that the voltage in the resistor is

so, if Vref = 1 V

we have the schematic shown in the second image, in the first one we can see how the input signal in orange increase and the levels of the comparators change when the input signal overcome

This analysis is posible because of the resistors are the same value in the case of Flash ADC, if the resistors are different to find the voltage drop, take the current and multiply by each resistor and add the voltage under the resistor that you want to know the voltage drop, something like this...