OK4 inputs = 16 states. I would use the raw Gray code as an index into a 16 character array of segment patterns. No other fancy translation required.
OKYou just generate a 10 entry table in the micro memory to map the Gray code into the 7 segment signals needed for a 0 to 9 display.
Fore example for a Gray code of 3 you would convert 0010 to ABCDG (7-segment 3).
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Thank you for you responseLike @crutschow says except sort the table on the raw gray code value so that it provides a direct index into the segment patterns for each digit.
The PDF shows how I would do it - a Gray to 7 segment decoder.