the maximum (or minimum) whole number a computer or program can store, typically defined by the number of bits (e.g., 32-bit, 64-bit) and whether it's signed (positive/negative) or unsigned (positive only); the common 32-bit signed integer max is 2,147,483,647, while a 64-bit signed integer goes up to about 9 quintillion, with larger numbers causing integer overflow (wrapping around or causing errors). Computers use bits (0s and 1s) to represent numbers; a fixed number of bits (like 32 or 64) limits how many unique values can be stored. When a calculation exceeds the maximum, integer overflow occurs, causing the number to "wrap around" (like a car odometer) or trigger an error, depending on the system.
32-bit Signed Integer: Max: 2,147,483,647 (\(2^{31}-1\)). Min: -2,147,483,648 (\(-2^{31}\)). Common Issue: The Year 2038 Problem, where time values exceed this limit. 64-bit Signed Integer: Max: 9,223,372,036,854,775,807 (\(2^{63}-1\)). Min: -9,223,372,036,854,775,808 (\(-2^{63}\)). 64-bit Unsigned Integer: Max: 18,446,744,073,709,551,615 (\(2^{64}-1\)) (no negatives).
