TLDR: The maximum representable range refers to the largest and smallest values a particular data type or system can accurately represent. This range is determined by factors like the number of bits used, the encoding scheme, and the arithmetic model (e.g., integer or floating-point). For example, in a 32-bit signed integer, the maximum representable range is from -2,147,483,648 to 2,147,483,647, while in 64-bit double-precision floating-point numbers (as per IEEE 754), it extends to approximately ±1.8 × 10^308.

https://en.wikipedia.org/wiki/Integer_(computer_science)

In floating-point arithmetic, the maximum representable range is defined by the size of the exponent and significand fields in the data format. The IEEE 754 standard specifies subnormal numbers and infinity as special cases for values that fall outside the normalized range. Exceeding the maximum representable range in floating-point operations results in overflow, often represented as positive or negative infinity. Proper handling of these edge cases is crucial in fields like scientific computing, where precision and stability are critical.

https://standards.ieee.org/standard/754-2019.html

Understanding the maximum representable range is vital for developers to avoid computational errors, such as overflow or underflow. In Java, developers can use the `Integer.MAX_VALUE` or `Double.MAX_VALUE` constants to determine these limits programmatically. Tools like BigInteger and BigDecimal provide alternatives for handling values beyond native data type ranges. Awareness of these constraints helps ensure robust and reliable software, especially in applications requiring high precision and large-scale numerical computations.

https://docs.oracle.com/javase/tutorial/java/nutsandbolts/datatypes.html