A T34 PLT DEPARTED EYQ PRIOR TO RECEIVING IFR CLRNC AND ENTERED CLASS B AIRSPACE WITH A MALFUNCTIONING HSI AND GPS WITH AN INCOMPLETE DISTANCE DISPLAY.

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FILED IFR EYQ TO ADH WITH INSTRUCTIONS TO CONTACT HOUSTON APCH FOR CLRNC. NO RADIO CONTACT WITH APCH WHILE ON THE GND. DEPARTED VFR AT XA16 ON A MAG COURSE OF 356 DEGS. CALLED APCH BUT NO CONTACT. IMMEDIATELY AFTER DEP; I NOTICED THAT THE HSI APPEARED TO GIVE NORMAL READINGS. CROSS CHKING WITH THE GPS DISPLAY I CONCLUDED THAT THE HSI WAS GIVING ERRONEOUS READINGS. AGAIN CALLED APCH WITHOUT RESULT. THE GPS MOVING MAP DISPLAY INDICATES THE LIMITS OF CLASS B AIRSPACE. AS I PASSED WHAT I ASSUMED WAS THE OUTER RING I CLBED OUT TO HAVE A BETTER CHANCE OF CONTACTING APCH. THIS TIME RADIO CONTACT WAS ESTABLISHED. THE CTLR ADVISED THAT I WAS IN CLASS B AIRSPACE. SIMULTANEOUSLY; ANOTHER AIRSPACE RING APPEARED ON THE MOVING MAP DISPLAY. I WAS; OF COURSE; PAST THE 20 NM RING; NOT THE 30 NM RING. THE CTLR GAVE ME A CLRNC AND I PROCEEDED TO DEST WITHOUT RELYING ON THE SUSPECT HSI. A COMBINATION OF DIVIDED ATTENTION DUE TO INSTRUMENT FAILURE; DELAYED RADIO CONTACT; AND NAV SETUP NOT COMPATIBLE WITH CLASS B AIRSPACE IDENTIFICATION CONTRIBUTED TO THIS EVENT. SINCE I EXPECTED TO BE UNDER CTL ON AN INSTRUMENT FLT PLAN; THE LIMITS OF THE CLASS B AIRSPACE WERE NOT PRIMARY TO MY COCKPIT SETUP. AN IMPROVEMENT IN THE MOVING MAP DISPLAY MIGHT BE TO PROVIDE A BETTER INDICATION OF WHICH RING THE AIRSPACE IS DISPLAYED.