I need to design a digital circuit that will output logic 1 and lit an LED when the input analog voltage is within a certain range (say 2-5 volt) and will output logic 0 elsewhere. A schematic would be very helpful. Thanks in advance!
What you need is called a "window comparator". Follows a link to one of many many ways of doing it. Do a search with windows comparator and you will find a lot of different circuits to opt from.
I think the chip you need is
TCA965 , by siemens if i'm not mistaking .
You can set the lower and higher trippoint and it gives you a signal inside window or without to high or without to low .
I must have a data sheet here somewhere , i'll see if i can find it .
Check out Poptronix magazine they recently, within the last couple of years, had a column that addressed comparator usage. If that doesn't prove fruitful I think I have a couple of old designs I could share.