Integer overflow (C++)

Unsigned integer

Range: [0,255]
Binary:   00000000 =++=> 00000001 =++=> ... =++=> 11111111
Hex:      0x00     =++=> 0x01     =++=> ... =++=> 0xFF
Interpr.: 0        =++=> 1        =++=> ... =++=> 255

“Unsigned integers shall obey the laws of arithmetic modulo 2^n where n is the number of bits in the value representation of that particular size of integer.” (C++ Standard (N4713) – 6.7.1.4)

#include <stdint.h>

int main()
{
  uint8_t i = 255;
  i++; // definded behavior, i = 0 (= 256 % 2^8)
  return 0;
}

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Signed integer
Signed Magnitude (old processors)

Range: [-127,127]
Binary:   00000000 =++=> ... =++=> 01111111 =++=> 10000000 =++=> ... =++=> 11111111
Hex:      0x00     =++=> ... =++=> 0x7F     =++=> 0x80     =++=> ... =++=> 0XFF
Interpr.: +0       =++=> ... =++=> +127     =++=> -0       =++=> ... =++=> -127

One’s complement (old processors)

Range: [-127,127]
Binary:   00000000 =++=> ... =++=> 01111111 =++=> 10000000 =++=> ... =++=> 11111111
Hex:      0x00     =++=> ... =++=> 0x7F     =++=> 0x80     =++=> ... =++=> 0XFF
Interpr.: +0       =++=> ... =++=> +127     =++=> -127     =++=> ... =++=> -0

Two’s complement (new processors)
–> Advantage: Basic arithmetic operations are identical to the unsigned ones.

Range: [-128,127]
Binary:   00000000 =++=> ... =++=> 01111111 =++=> 10000000 =++=> ... =++=> 11111111
Hex:      0x00     =++=> ... =++=> 0x7F     =++=> 0x80     =++=> ... =++=> 0XFF
Interpr.: +/-0     =++=> ... =++=> +127     =++=> -128     =++=> ... =++=> -1

“If during the evaluation of an expression, the result is not mathematically defined or not in the range of representable values for its type, the behavior is undefined.” (C++ Standard (N4713) – 8.1.4)

#include <stdint.h>

int main()
{
  int8_t i = 127;
  i++; // undefined behavior, but often i = -128 (2's comp.)
  return 0;
}

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References
C++ Standard (N4713)