Final answer:
In a 2-byte signed integer representation where the leftmost bit indicates the sign, the largest possible positive integer is 32767.
Step-by-step explanation:
If 2 bytes (16 bits) is used to represent an integer and the leftmost bit is used for the sign, then we have 15 bits to represent the magnitude of the number. In the binary numeral system, when all 15 bits are set to 1, this corresponds to the largest possible positive integer that can be represented in such a format.
In binary, the largest number you can represent with 15 bits is 111111111111111, which is equal to 32767 in decimal. Therefore, the largest possible integer that can be represented in 2 bytes with the leftmost bit used for the sign is 32767.