Combinational Logic High for Range

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I need to use combinational logic to produce a high ouput for a certain range of values. I have and anaolgue signal which i have converted to a 12 bit digital signal, I need an LED to be turned on when the analogue signal is above a certain voltage.

I have the digital value (101001110100 = 6V), now I need the LED to be turned on for all values between this and 111111111111. SO i guess what I am asking is there any shortcut for implenenting logic for all values above a specified one. I hate to think that I am going to have to go through and write an SOP for all the intermeiate values, and then it is impossible to put on a karnaugh map to simplify (humanly impossible).

So does anyone know of a shortcut for implementing this seemingly simple logic function?
Many Thanks
 
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couldn't you just use a comparator?
 
Comparator was used to create the 12 bit signal, now i must use the 12 bit digital signal to illuminate an LED when the analogue input is >6V.

Combinational logic must be used to illuminate the LED, it is all i am able to use. No comparator available for this part of the circuit.

I am thinkin of splitting up the 12 bit signal into 3 4 bit codes, but this also causes a lot of complications in the implementation. Thanks for replying hough, it is the best idea, unfortunate i cannot use it.
 
OK for anyone interested what i did in the end was made comb logic for the 4 MSB's when they are above 1010 high output, then ANDed that with and OR for both when 1010 and the second set of 4 bits that were below 0111, and when the MSB's are 1010, second 4 0111, and the 4LSB's below 0100. Yeah that was a bit much for one sentence, but if anyone is interested i can post the logic diagram when I've done it. Cheers.