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The int keyword in C++ designates a fundamental, built-in numeric data type used to represent signed, exact-value integers. By default, int is a signed type. As of C++20, the standard mandates that signed integers use Two’s Complement representation, where the most significant bit acts as a sign bit with a negative weight, and the remaining bits contribute to the overall value.

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Memory Allocation and Data Models

The C++ standard does not prescribe a fixed size in bytes for int. Instead, it dictates minimum width requirements based on the underlying architecture’s data model.
  • Standard Guarantee: The standard guarantees that an int will be at least 16 bits wide. Note that this does not strictly equate to 2 bytes; the standard defines size in terms of char (bytes), and the number of bits in a byte (CHAR_BIT) is only guaranteed to be at least 8.
  • Modern Architectures: In nearly all modern 32-bit and 64-bit data models (such as ILP32, LP64, and LLP64), int is implemented as a 32-bit integer.

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Syntax and Initialization

C++ supports multiple initialization paradigms for int. Uniform (brace) initialization is the modern standard as it strictly prohibits narrowing conversions. 
// Declaration without initialization.
// Contains an indeterminate garbage value if it has automatic storage duration (local block-scope).
// Zero-initialized if it has static or thread storage duration (namespace/global scope).
int uninitialized_val;

// Copy initialization
int copy_val = 42;

// Direct initialization
int direct_val(42);

// Uniform / Brace initialization (C++11 onwards)
int brace_val{42}; 

// Zero-initialization via empty braces
int zero_val{};

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Value Range and Representation

Because C++20 requires Two’s Complement representation, the range of an int is strictly determined by its bit width (nn), calculated as −2n−1-2^{n-1} to 2n−1−12^{n-1} - 1. Assuming the standard modern 32-bit implementation:
  • Minimum Value: -2,147,483,648
  • Maximum Value: 2,147,483,647
These limits can be queried programmatically at compile-time using the <limits> header: 
#include <limits>

constexpr int min_val = std::numeric_limits<int>::min();
constexpr int max_val = std::numeric_limits<int>::max();

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Type Modifiers

The int type serves as the base for several modified integer types, which alter either the sign representation or the memory allocation:
  • Sign Modifiers:
    • signed int (Identical to int)
    • unsigned int (Uses all bits for magnitude, shifting the 32-bit range to 0 through 4,294,967,295)
  • Size Modifiers:
    • short int (Guaranteed minimum 16 bits)
    • long int (Guaranteed minimum 32 bits)
    • long long int (Guaranteed minimum 64 bits)
Note: When using modifiers, the int keyword itself can be omitted (e.g., unsigned is synonymous with unsigned int).

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Overflow Behavior

According to the C++ standard, signed integer overflow invokes undefined behavior (UB). If an operation causes an int to exceed its maximum or minimum representable value, the compiler is permitted to optimize out the check or execute unpredictable instructions. This contrasts with unsigned int, which is guaranteed to wrap around modulo 2n2^n.
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