The reason for this lies in how signed integers are typically represented in computers: two’s complement.
Two’s Complement: In two’s complement representation, the most significant bit (leftmost bit) is used to represent the sign of the number.
If the most significant bit is 0, the number is positive.
If the most significant bit is 1, the number is negative.
Range of Values:
With 16 bits, we have 2^16 = 65536 possible combinations.
However, we need to divide this range to accommodate both positive and negative numbers.
This results in:
Positive range: 0 to 2^15 – 1 (0 to 32767)
Negative range: -2^15 to -1 (-32768 to -1)
In summary:
The limitation of the maximum value of an int16 to 32767 arises from the need to represent both positive and negative numbers within the available 16 bits using two’s complement notation.