AN AMERICAN YANKEE LOW TIME PVT PLT WITH A MALFUNCTIONING MODE C CONFUSES THE TWR CTLR WHEN GIVING AN ERRED POS RPT AS 6 MI SW OF THE ARPT WHEN ACTUALLY 6 MI NW OF LGB; CA.

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VFR INBOUND FOR LGB; ENDED UP ON SHORT FINAL FOR THE WRONG RWY. FIRST CONTACT WITH LGB TWR WAS 6 MI NW; BUT I INCORRECTLY RPTED MY POS AS 6 MI SW. ALSO; UNKNOWN TO ME; MY MODE C RPTED 100 FT WHEN I WAS AT 2000 FT. BASED ON THIS INFO; THE CTLR THOUGHT I WAS A POLICE HELI THAT HE HAD ON HIS RADAR SCREEN. HE GAVE ME VECTORS THAT WERE MEANT TO TAKE ME TO RWY 25L; BUT SINCE I WAS NOT WHERE HE THOUGHT I WAS; HIS VECTORS LINED ME UP FOR RWY 34L. WHEN I WAS ON SHORT FINAL; I READ THE PAINTED NUMBERS '34L;' AND IMMEDIATELY INFORMED THE TWR; AND OFFERED TO GO AROUND. TWR CONCURRED; AND GAVE ME A L TURN TO 250 DEGS. THEY THEN GAVE ME A L 180 DEG TURN TO 070 DEGS; WHICH PUT ME ON DOWNWIND FOR RWY 25L. AT THIS POINT; I BECAME REORIENTED; FLEW A NICE PATTERN; AND LANDED WITHOUT FURTHER DIFFICULTY. THEN CAME THE DREADED CALL 'CALL THE TWR AFTER YOU SHUT DOWN.' I CALLED THE TWR AND HAD A TALK WITH THE TWR SUPVR. EXPLAINED EVERYTHING. HE WAS VERY NICE; AND TOLD ME TO BE CAREFUL. CONTRIBUTING FACTORS: 1) SITUATIONAL AWARENESS (RPTED WRONG POS). 2) XPONDER GAVE WRONG ALT; CONFUSING THE CTLR; AND ADDED TO HIS STRESS LEVEL. THE TWR WAS VERY BUSY AT THAT TIME.