x86 machine code (MS-DOS .COM format), 53 4949 44 bytes
Edit: Saved 4 bytes by eliminating a redundant CALL/RET and 5 bytes by outputting via INT 29H.
Input is taken from the command line: no input will search for NUL (hex 00H). Result is in the form "00/00" (i.e. "03/53"44" for an input of "!)").
A0 82 00 B9 312C 00 33 D2 BF 00 01 F2 AE E3 03 42 EB F9 8B C2 E8 07 00 B2B0 2F CD 2129 B8 312C 00 D4 0A 8B D0 81 C205 30 30 B4 02 86 F2E0 CD 2129 86 F2E0 CD 2129 C3
IDEAL
MODEL TINY
CODESEG
ORG 100H
PSIZE EQU PEND-MAIN
PLEN EQU PSIZE+1 ; Loop needs to be one longerlarger so we can break aton CX=0
MAIN:
MOV AL,[0082H] ; Get search value from the command line
MOV CX,PLEN
XOR DX,DX
MOV DI,100H ; Start search from the beginning of the program
CLOOP:
REPNZ SCASB ; Search for value
JCXZ CDONE ; Exit when at of end of string
INC DX
JMP CLOOP
CDONE:
MOV AX,DX
CALL DISPNUM
MOV DL AL,'/'
INT 21H 29H
MOV AX,PSIZE
; Fallthrough to print last number and exit
DISPNUM:
AAM ; Convert value to unpacked BCD (AH:AL)
MOV DX,AX
ADD ADD DXAX,3030H ;
Convert to ASCII
XCHG MOV AH,2AL
XCHGINT DH,DL ; Flip digits to29H
prepare for printing
XCHG INT 21HAH,AL
XCHG DH,DL
INT INT 21H29H
RET
PEND:
END MAIN
ENDS