AN IFR DEPARTING BE36 MAKES A WRONG TURN AFTER TKOF RESULTING IN LTSS WITH A PREVIOUS IFR DEP. BE36 CESSNA.

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THERE WAS ONLY 1 SUPVR ASSIGNED FOR THE WHOLE DAY; AND HE WAS ASSIGNED A 10-6 SHIFT. THEREFORE; AN ATC SPECIALIST WAS REQUIRED TO COVER THE SUPERVISORY POS AS A CIC. IN ORDER TO ACCOMMODATE BREAKS; I WAS ASSIGNED TO WORK THE GND CTL; CLRNC DELIVERY; AND FLT DATA POS COMBINED. HISTORICALLY; CLRNC DELIVERY IS BUSY AT FIRST WITH THE XA30 AM DEPS AND THEN GND CTL BEGINS TO GET BUSY AT AROUND XA20. IN ADDITION; GND CTL HAS TXWY INSPECTIONS BY CITY OPS VEHICLES AT AROUND THIS TIME. THE WX WAS IFR AND INCLUDED IN MY RESPONSIBILITIES AT FLT DATA POS IS MONITORING THE WX. A BE36 REQUESTED A CLRNC VFR ON TOP. I TYPED IN A CLRNC VIA THE FDIO; HAD A FEW OTHER CALLS AND DUTIES TO PERFORM AND THEN ISSUED A CLRNC WITH A CLRNC LIMIT OF THE SJC VOR AND IN ACCORD WITH 7110.65J CHANGE 3 CH 7-3-1B.5; BUT FAILED TO ISSUE A L TURN HDG 140 DEGS AS INSTRUCTED IN SJC/BAY TRACON LOA. THE PLT READ BACK THE CLRNC WITH AN INCORRECT SQUAWK READBACK. I CORRECTED THE SQUAWK AND THE PLT READ IT BACK CORRECTLY. SOMETIME AFTER THIS THE PLT CALLED FOR TAXI INSTRUCTIONS. I ISSUED INSTRUCTIONS TO RWY 30R. THEREAFTER; THE LCL CTLR OBTAINED A RELEASE FROM BAY TRACON AND DEPARTED THE BE36. THE LCL CTLR ISSUED THE L TURN HDG 140 DEGS TO THE PLT AND THEN TO CONTACT BAY DEP. THE PLT ACKNOWLEDGED; BUT DID NOT READBACK. HE THEN TURNED R INSTEAD OF L AND CAME WITHIN 3 MI OF A PREVIOUS CESSNA ON A SUNOL 4 DEP SID. I FEEL THIS SIT COULD HAVE BEEN AVERTED IF THE POS WOULD NOT HAVE BEEN COMBINED. I FEEL THE NORMAL STAFFING OF 2 SUPVRS FOR THE DAY COVERING OPENING TO XYPM WOULD HAVE MADE IT SO THAT THE POS COULD BE DECOMBINED. THE POS BEING COMBINED CAUSED A DIVISION OF CONCENTRATION CAUSED BY MONITORING AND MANAGING TOO MUCH INFO. I SHOULD HAVE CONCENTRATED ALL MY ATTN TO ISSUING THE CLRNC AND THE READBACK. THE LCL CTLR SHOULD HAVE GOTTEN A READBACK OF THE TURN INSTRUCTIONS. THE PLT SHOULD HAVE LISTENED MORE CAREFULLY AND IF HE HAD ANY DOUBTS AS TO THE DIRECTION OF THE TURN; HE SHOULD HAVE ASKED THE LCL CTRL TO REPEAT THE INSTRUCTIONS.