CS

Why would int 53191 become -12345 after truncating to short

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explain the truncation more detailed

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Let’s dive deeper into what happens when an int is truncated to a short in your program.

Key Background Concepts

  1. Size of Data Types:

    • int: Typically 4 bytes (32 bits) on most modern platforms.
    • short: Typically 2 bytes (16 bits).
    • The exact sizes depend on the platform and compiler but follow the standard: sizeof(short) ≤ sizeof(int).

  2. Truncation:

    • When you cast a larger data type (int, 32 bits) to a smaller data type (short, 16 bits), only the least significant bits (LSBs) that fit into the smaller type are retained.
    • Any bits beyond the size of the smaller type (the most significant bits, MSBs) are discarded.

  3. Signed Representation:

    • short is a signed type, meaning it uses the most significant bit (MSB) as the sign bit:
      • 0: Positive number.
      • 1: Negative number (two’s complement representation).

Detailed Step-by-Step Analysis of Truncation

Step 1: Initial Value of x

  • x = 53191 (in decimal).

  • In hexadecimal, 53191 is represented as:
    0x0000CF47 (32 bits).

    1

    0000 0000 1100 1111 0100 0111 (binary)

Step 2: Casting x to short (sx)

When x is cast to a short, only the least significant 16 bits are kept:

1

1100 1111 0100 0111 (binary)
  • This corresponds to 0xCF47 in hexadecimal.

Now, the value is interpreted as a 16-bit signed number:

  1. The MSB (1) indicates that the value is negative (two’s complement).
  2. To find the value of a negative number in two’s complement:

    • Invert the bits:

      1

      0011 0000 1011 1000

    • Add 1 to the result:

      1

      0011 0000 1011 1001 (binary) = 12345 (decimal)

    • The result is -12345.

So, sx becomes -12345 after truncation.

Step 3: Assigning sx to y

  • When sx is assigned to y (an int), no truncation occurs because int can hold all the values of short.
  • The value of sx (-12345) is preserved, so y = -12345.

Summary of Truncation

  • Before Truncation: x = 53191 (0x0000CF47 in 32 bits).
  • After Truncation to short: Only the lower 16 bits are kept: 0xCF47.
  • Interpretation as a Signed 16-bit Integer: 0xCF47 is -12345 in two’s complement.
  • Value in y: The value -12345 is preserved when expanded back to 32-bit int.

This truncation occurs because casting between different data types in C operates at the bit level without considering the original value’s “semantic” meaning.