SMA X ISSUED WRONG VECTOR HDG AFTER DEP HAD LTSS FROM SMA Y. SYS ERROR.

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I WAS WORKING SCK TWR; ALL POSITIONS COMBINED AT THE FLT DATA POS. I HAD 3 ACFT ON APCH WHEN THE SMA X REQUESTED A CLRNC TO TAXI AND PICK UP AN IFR FOR AN APCH AT SCK; THEN IFR TO FAT. AN SMA RPTED MISSED AT THE SAME TIME SMA X WAS MAKING HIS REQUEST. I TOLD THE SMA TO CONTACT DEP AND THEN ADVISED SMA X I HAD HIS CLRNC. I ISSUED THE CLRNC FOR THE SCK ARPT AND Told HIM TO EXPECT CLRNC FOR FAT ON THE DOWNWIND. IN ISSUING THE CLRNC I GAVE A WRONG INITIAL HDG OF 200 DEG INSTEAD OF 050 DEG. THE PLT READ IT BACK AND I MISSED IT ON THE READBACK AS I WAS TYPING IN THE ACFT NUMBER AND TYPE INTO THE ARTS SYS. SMA X TOOK OFF AND TURNED TO A HDG OF 200 WHICH BROUGHT HIM BACK OVER THE ARPT. SMA Y WAS CLBING OUT ON RWY HDG AND THEY WERE LESS THAN 500 FT ALT APART AND LESS THAN 1/2 MI. THEY WERE BOTH IMC. SMA X WAS TURNED AWAY BY THE APCH CTLR. ONE OF THE CONTRIBUTING FACTORS IS THAT WHEN LCL IS COMBINED AT GND; THE GND FREQ IS EXTREMELY WEAK. THIS PLUS THE DIVERSION OF COMPUTER ENTRIES AND LISTENING ONLY TO WHAT I WANTED TO HEAR COULD HAVE DEVELOPED INTO DISASTER. POSSIBLE SOLUTIONS: HAVE MAINT INCREASE GND CTL VOLUME; WRITE CLRNC ON BLANK STRIP EVEN WHEN WORKING ALONE AS MEMORY JOGGER.