PVT PLT OF AN SMA SEL PENETRATED CLASS B AIRSPACE WHEN HE BELIEVED THAT HE HAD RECEIVED A CLRNC.

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I DEPARTED PVU AT APPROX XA45 LCL TIME IN A C-152/U ON A VFR FLT PLAN FROM PVU TO LGU. AT THE SOUTHERN TIP OF THE CLASS B AT A CHK POINT KNOWN AS 'POINT OF THE MOUNTAIN' I RADIOED TO SLC APCH MY INTENTIONS; LOCATION AND THAT I HAD CURRENT ATIS. I WAS GIVEN A XPONDER CODE OF WHICH I DIALED IN. I WAS ALSO TOLD TO MAINTAIN MY ALT OF 6500 AND REMAIN E OF INTERSTATE 15; THE EASTERN BOUNDARY OF THE SLC CLASS B. I WAS NOT ADDRESSED AGAIN. APPROX 15 MINS LATER; 5-10 MINS NE OF SLC ARPT I RADIOED TO SLC APCH ASKING IF I HAD BEEN FORGOTTEN. I WAS ASKED FOR MY FULL N-NUMBER AND MY LOCATION. I RESPONDED THE ACFT INFO AND THAT I WAS JUST NE HDG NBOUND FROM THE S IN THE BOUNTIFUL (A CITY) AREA. ACCORDING TO MY OWN CALCULATIONS I WAS JUST ON THE EASTERN BOUNDARY OF THE CLASS B IN THAT AREA WHICH GOES FROM 10000 FT TO THE SURFACE. I WAS MAKING MY WAY AROUND THE BOUNDARY; AVOIDING THE MOUNTAINS ALSO ON THE E SIDE. THE CTLR ANSWERED THAT I WAS IN THE CLASS B WITHOUT A CLRNC AND TO TURN 30 DEGS R SO HE COULD INTERCEPT ME ON RADAR. APPROX 10-20 SECONDS LATER HE RADIOED THAT HE HAD ME ON RADAR CONTACT AND TOLD ME ONCE AGAIN I WAS NOT TO BE IN THE CLASS B WITHOUT A CLRNC. I TOLD HIM I HAD CODE DIALED IN AND HE SAID HE HAD NOTHING ON HIS SCREEN. I TUNED IT IN AGAIN; TRYING THE 'TST' FEATURE ON THE XPONDER AND HITTING THE 'IDENT' BUTTON. HE RESPONDED THAT HE STILL HAD NOTHING. APPARENTLY MY XPONDER WAS INOP. HOWEVER; WHEN I RENTED THE ACFT; NO MENTION WAS MADE OF AN INOP XPONDER IN THAT ACFT; EITHER VERBALLY OR WRITTEN. I HAD NO WAY OF KNOWING THAT MY XPONDER (THE ONE IN THE ACFT) WAS INOPERABLE. I WAS GIVEN THE TWR FREQ FOR THE NEXT PLACE (HILL AFB) WHO THEN PUT ME THROUGH (AFTER REACHING THEIR NORTHERN BOUNDARY) TO OGD TWR; A CLASS D. I THEN PROCEEDED TO LGU WHERE I CALLED TRACON AND RECEIVED A 1 TIME CLRNC TO COME BACK TO PVU; AND INSTRUCTIONS ON HOW TO DO IT. TO ME THE PROBS WERE: AN INOP XPONDER THAT WAS NOT KNOWN ABOUT. THERE IS NO WAY OF LETTING THE CTLR KNOW WHO HE HAS TALKED TO; AND WHICH CODES THAT HE HAS ASSIGNED DON'T COME UP; THEREBY ALERTING HIM TO A POTENTIAL PROB. I USUALLY RECEIVE A CLRNC TO ENTER THE CLASS B ALONG WITH DIRECTIONS TO FLY. APPARENTLY; I RECEIVED NO CLRNC WITH MY INITIAL DIRECTIONS; AND BECAUSE I WAS NOT VISIBLE DUE TO MY INOPERABLE XPONDER; THE CTLR NOR I KNEW WE WEREN'T 'COMMUNICATING' SO TO SPEAK ELECTRONICALLY. I ONLY FOUND OUT ABOUT THE XPONDER WHEN IT WAS TOO LATE. OTHERWISE I COULD HAVE TAKEN ACTION TO AVOID THE CLASS B ALTOGETHER.