PA28 PLT INBOUND TO NXX MISINTERPRETS APCH CTLR'S INSTRUCTIONS AND DSNDS INTO NXX CLASS D WITHOUT A CLRNC.

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I REQUESTED AIR TFC SVCS FROM MCGUIRE APCH (127.5) WHO ASSIGNED ME A SQUAWK CODE AND HANDED ME OFF TO PHILADELPHIA APCH (123.8). PHILADELPHIA APCH INSTRUCTED ME TO MAINTAIN 4000 FT AND PROCEED ON COURSE. THE FREQ WAS FAIRLY BUSY. WHEN I WAS APPROX 12 MI FROM N10 AND 5 NM N OF NXX; I REQUESTED A DISCRETIONARY DSCNT INTO N10. PHILADELPHIA APPROVED DSCNT AS REQUESTED (MAINTAIN VFR); BUT ADVISED THAT I HAD SBOUND TFC AT 12 O'CLOCK POS; 3 MI AT 3500 FT. I INDICATED I DID NOT HAVE THE TFC IN SIGHT; AND WOULD PREFER TO DELAY MY DSCNT UNTIL I HAD PASSED THE TFC. PHILADELPHIA INSTRUCTED ME INSTEAD TO TURN COURSE 180 DEGS; VECTORS FOR TFC. THE 180 DEG VECTOR HAD PUT ME ABOVE NXX'S CLASS D AIRSPACE. PHILADELPHIA APCH; FREQ 123.8; IS ALSO APCH CTL FOR NXX. SHORTLY AFTER THIS; I SAW THE CESSNA AT 2:30 O'CLOCK POS; AND SLIGHTLY BELOW ME. I INFORMED PHILADELPHIA THAT I HAD THE TFC. PHILADELPHIA INFORMED ME TO 'MAINTAIN VFR SEPARATION WITH TFC; DSND AT DISCRETION; PROCEED ON COURSE; AND CONTACT PHILADELPHIA ON 126.85.' I THOUGHT PHILADELPHIA HAD CLRED ME INTO NXX'S (WILLOW GROVE) CLASS D AIRSPACE (TOP 2900 FT); AND WAS COORDINATING WITH THE TWR. I TURNED ON COURSE AND EXPEDITED MY DSCNT TO 2500 FT TO INSURE ADEQUATE TFC SEPARATION. I CONTINUED A GRADUAL DSCNT TO 1500 FT. WHEN THE FREQ WAS CLR; I CHKED IN WITH PHILADELPHIA ON 126.85. THE NEW CTLR INFORMED ME THAT I HAD NOT BEEN CLRED INTO NXX CLASS D AIRSPACE. WHEN I REPEATED MY CLRNC; THE NEW CTLR INFORMED ME THAT OTHER CTLR ALSO GAVE ME A CLRNC LIMIT TO 'REMAIN CLR OF CLASS D AIRSPACE.' SHE SUGGESTED THAT MAYBE I DIDN'T HEAR IT.