MISINTERPING THE DIRECTION OF A GIVEN 30 DEG TURN LEADS TO A WRONG DIRECTION OF TURN AND A TFC CONFLICT.

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OUR ACFT WAS JUST CLRED TO TURN 30 DEG L (WHERE DISCREPANCY WAS) AND TO CLB TO FL310. I WAS IN THE R SEAT; ACKNOWLEDGED THE CLRNC; AND WAS IN THE PROCESS OF SETTING THE NEW ALT IN THE ALERTER; TURNING MY HDG BUG; AND TUNING UP THE DNV VOR; WHERE WE WERE TO BE CLRED TO NEXT. ALL OF WHICH TOOK APPROX 30-40 SECONDS. UPON FINISHING I NOTICED THAT WE WERE 30 DEGS R OF PREVIOUS HDG. I WAS OPENING MY MOUTH TO QUESTION THE PF OF THE DISCREPANCY WHEN THE TCASII HAD A VISUAL TA (COLOR OF TARGET CHANGED); AT THE SAME TIME THE CTLR ASKED IF WE HAD STARTED OUR TURN AND IMMEDIATELY ISSUED A TURN TO 080 DEGS. WE ROLLED INTO A 45 DEG BANK L TURN; AS I DECREASED THE SCALE ON THE TCASII AT 5 NM. HE WAS RIGHT ON THE EDGE OF THE CIRCLE AND AT 2 O'CLOCK POS. SOMEWHERE IN OUR TURN; THE OTHER ACFT WAS GIVEN A TURN TO ITS L. (AT THAT TIME THE ESTIMATED 5 NM AND -200 FT WAS OBSERVED.) AFTER A FEW MORE SECONDS; BOTH ACFT WERE CLRED BACK ON COURSE. THE COMMERCIAL ACFT (I BELIEVE TO BE AN ACR Y) QUESTIONED IF WE HAD EXCEEDED 5 NM OF CLRNC AND THE CTLR SAID IT DID NOT APPEAR TO HAVE BEEN EXCEEDED; BUT WITH THE TURNING; WASN'T EXACTLY SURE. HE ALSO SAID NOTHING 'CAME DOWN FROM THE WASH-OUT DESK' SO IT APPEARED TO BE OK. THE PROB WAS DISCOVERED BY ALL 3 PARTIES AT APPROX THE SAME TIME. THE ACFT HAD TCASII ALERTS; AND THE CTLR BEING ALERT; NOTICED. THE PLT FLYING AT THE TIME SAID HE WAS SURE HE HAD HEARD RIGHT. HE DID NOT REPEAT THE CLRNC TO ME AFTER I ACCEPTED IT; WHICH MAY HAVE CAUGHT THE DISCREPANCY. I LET MYSELF GET BUSY AND DIDN'T FOLLOW THROUGH WITH MAKING SURE THE CLRNC WAS CARRIED OUT; WHICH WOULD HAVE ALSO CAUGHT THE DISCREPANCY. IN SHORT; THE PROB COULD HAVE BEEN RESOLVED EARLIER; OR AT LEAST NOTICED; AND THE CLRNC QUESTIONED AT AN EARLIER TIME. I WOULD ALSO NOTE THAT I KNOW THAT OUR CREW HAD BEEN UP SINCE XA00 AND FLOWN TO FCM; WAITED ALL DAY; AND DEPARTED THERE (FCM) AT XL00 TO RETURN TO OUR HOME. AFTER WAITING IN THE FBO THERE ALL DAY BOTH THE PF AND I WERE ACKNOWLEDGING THAT WE WERE TIRED AND FELT SLOW. I COULD ALSO SAY THAT IT IS NORMAL FOR THE PF TO REPEAT THE CLRNC AND FOR THE PNF TO CHK FOR DISCREPANCY. I KNOW I USUALLY (ALMOST ALWAYS -- UNLESS BLATANTLY OBVIOUS) CHK THE PF'S ACTIONS. SO; I MAY SAFELY SAY FATIGUE WAS AT LEAST IN SOME RESPECT A FACTOR. I FEEL MORE FATIGUE OR 'BRAIN DEAD' AFTER SITTING AROUND ALL DAY AFTER GETTING UP EARLY THAN IF I AM BUSY FLYING ALL DAY. THE BRAIN AND PHYSICAL INACTIVITY CATCH UP WITH ME; AS WELL AS ANYONE. THAT'S MY PERSPECTIVES AND INSIGHTS ON THE SIT. FATIGUE WILL SOUND AN ALARM IN MY SUBCONSCIOUS EVEN MORE NOW.