Final answer:
The largest signed integer that can be stored in 32 bits is 2,147,483,647, which is due to using one bit for the sign and the remaining 31 bits for the magnitude of the number in binary form.
Step-by-step explanation:
The largest signed integer that can be stored in 32 bits is 2,147,483,647. To understand why that is, we should review how numbers are represented in binary form inside a computer. Signed integers use one bit (usually the most significant bit) to represent the sign of the number. With the highest bit reserved for the sign (0 for positive, 1 for negative), this leaves 31 bits for the magnitude of the number.
In binary, a 32-bit signed integer's largest positive value is represented as 01111111 11111111 11111111 11111111, where the initial '0' signifies that the number is positive. This binary number equates to the decimal number 2,147,483,647. It's important to note that the range for 32-bit signed integers is -2,147,483,648 to 2,147,483,647 because the negative range includes an extra value due to how binary two's complement works.