C210 PLT HAD A RWY INCURSION AFTER LNDG AT PDK.

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AFTER LNDG ON RWY 20L AT PDK ARPT; TWR ADVISED ME TO 'TURN R NEXT TXWY; CROSS RWY 20R; CONTACT GND ON THE OTHER SIDE.' I TURNED ONTO THE TXWY REFERRED TO; AND WAS ANTICIPATING XING A RWY (20R). I CAME TO AN INTERSECTING TXWY AND GAVE WAY TO A TAXIING ACFT ON THAT TXWY. I ALSO SAW THAT MY TXWY DID NOT CONTINUE STRAIGHT AHEAD; BUT RATHER ANGLED TO THE L; AND SLIGHTLY OFF OF A STRAIGHT AHEAD PATH. I SAW A RWY IN THE DISTANCE WHICH I ASSUMED TO BE RWY 20R (LATER FOUND TO BE RWY 24); AND SO I THOUGHT I COULD TURN ON TO THE INTERSECTING TXWY AND CONTACT GND AT THAT POINT; SINCE THE FBO I WAS GOING TO WAS ON MY IMMEDIATE R (AND NOT ON THE OTHER SIDE OF THE RWY THAT I MISTOOK FOR RWY 20R). WHEN I CONTACTED GND; THEY INFORMED ME OF MY MISTAKE. LATER; WITH GND CTL ON THE PHONE AND THE ARPT DIAGRAM IN FRONT OF ME; I COULD SEE THAT I HAD ALREADY 'CROSSED' RWY 20R BY THE TIME I HAD REACHED THE INTERSECTING TXWY THAT I THEN TURNED ONTO; BUT DID NOT SEE RWY 20R BECAUSE I WAS AT THE VERY END OF RWY 20R AND IT EXTENDED ONLY TO MY L. THE TWR'S INSTRUCTIONS COULD HAVE BEEN STATED MORE CLRLY TO ALERT ME THAT I WOULD NOT BE 'XING' RWY 20R ON THE TRADITIONAL SENSE; HOWEVER IF I HAD THE ARPT DIAGRAM IN FRONT OF ME (INSTEAD OF FOLDED UP IN MY FLT BAG!) IT WOULD HAVE BEEN OBVIOUS TO ME BEFORE I HAD GONE TOO FAR. WHEN IN DOUBT; I SHOULD HAVE ASKED FOR DIRECTIONS.