If it were me, I'd make a one chip solution using an 8 pin DIP PIC processor with an internal clock an no other parts except a resistor and the LED. The code is trivial and simply subtracts (compares) the four bit input with the four possible bit patterns in a continuous repeating sequence. When a hit is made, the subtraction equals zero and the resulting zero status bit is used to set the output port true lighting the LED. This conditionis is latched true and remains that way through each sequence. If there is no hit or all hits are removed, the resulting non zero status clears the latch and the LED goes off.
Hey, I like your solution too Petrus! Yes, A-F is not supposed to occur as it is fed from a BCD counter. The OP used a 1of 10 decoder though I preferred to go after it with low level logic. That was a tiny bit of fun and a trip down memory lane!
And you just pick the outputs you need. If you need to light the _same_ LED for any of the four, just connect four diodes, cathodes to the chip pins, and all four anodes to the LED cathode, and adjust your resistor for the other diode drop.
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