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How do I rotate a bit?

Published in Bitwise Operations 2 mins read

Rotating a bit means shifting a bit within a fixed-size data type (like an integer) and "wrapping around" the bit that's shifted off one end to the other. Unlike a regular shift (left or right), no bits are lost; instead, they are circulated within the value.

Understanding Bit Rotation

Bit rotation operations move bits within a variable. The bits shifted off one end are re-inserted at the other end, preserving all the original bits. There are two primary types of bit rotation:

  • Rotate Left: Bits are shifted to the left, and the leftmost bit becomes the rightmost bit.
  • Rotate Right: Bits are shifted to the right, and the rightmost bit becomes the leftmost bit.

Implementing Bit Rotation

The exact implementation depends on the programming language and data type you're working with. Here's a common approach using bitwise operations, often found in C, C++, and similar languages:

Example: Rotating an 8-bit unsigned integer in C

Let's say you have an 8-bit unsigned integer variable c. Here's how to rotate it one bit to the left:

unsigned char c = 0b10110011; // Example value (binary representation)
unsigned char rotated_left;

rotated_left = (c << 1) | (c >> 7); // Rotate left by 1 bit

// Explanation:
// (c << 1):  Shifts all bits in 'c' one position to the left. The leftmost bit is lost (before OR).
// (c >> 7):  Shifts all bits in 'c' seven positions to the right.  This effectively isolates the original leftmost bit into the rightmost bit position.
// | :        The bitwise OR operator combines the results.

printf("Original: 0x%02X\n", c);
printf("Rotated Left: 0x%02X\n", rotated_left);

Rotating it one bit to the right:

unsigned char c = 0b10110011; // Example value (binary representation)
unsigned char rotated_right;

rotated_right = (c >> 1) | (c << 7); // Rotate right by 1 bit

// Explanation:
// (c >> 1):  Shifts all bits in 'c' one position to the right. The rightmost bit is lost (before OR).
// (c << 7):  Shifts all bits in 'c' seven positions to the left. This effectively isolates the original rightmost bit into the leftmost bit position.
// | :        The bitwise OR operator combines the results.

printf("Original: 0x%02X\n", c);
printf("Rotated Right: 0x%02X\n", rotated_right);

Generalization

For an n-bit value, rotating left by k bits:

rotated_left = (value << k) | (value >> (n - k));

Rotating right by k bits:

rotated_right = (value >> k) | (value << (n - k));

Considerations

  • Data Type Size: Ensure n accurately reflects the bit size of your data type (e.g., 8 for unsigned char, 16 for unsigned short, 32 for unsigned int).
  • Unsigned Types: These operations generally work best with unsigned integer types, as signed integers might introduce sign extension issues during the right shift. If using signed integers, be mindful of how your compiler handles right shifts.
  • Modular Arithmetic: To handle rotation amounts (k) larger than n, you can use the modulo operator (%) to effectively wrap the rotation amount within the range 0 to n-1. For example: k = k % n;

Built-in Functions

Some compilers and architectures provide intrinsic functions or assembly instructions for bit rotation. For example, certain versions of Visual C++ provide _rotl and _rotr intrinsics. Check your compiler's documentation to see if optimized rotation functions are available. These are often faster and more efficient than the bitwise operations.

Example in Python

Python does not have a fixed-size integer type like C. Therefore, rotation is often simulated using modular arithmetic and bit manipulation. The following demonstrates an equivalent rotation for a 32-bit integer:

def rotate_left(n, d, bits=32):
    """Rotates a 32-bit integer 'n' to the left by 'd' bits."""
    d %= bits  # Normalize rotation amount
    return ((n << d) | (n >> (bits - d))) & ((1 << bits) - 1)

def rotate_right(n, d, bits=32):
    """Rotates a 32-bit integer 'n' to the right by 'd' bits."""
    d %= bits  # Normalize rotation amount
    return ((n >> d) | (n << (bits - d))) & ((1 << bits) - 1)


num = 0b10101010101010101010101010101010  # Example 32-bit number
rotated_left = rotate_left(num, 5)
rotated_right = rotate_right(num, 5)

print(f"Original: {bin(num)}")
print(f"Rotated Left: {bin(rotated_left)}")
print(f"Rotated Right: {bin(rotated_right)}")

This Python example simulates a 32-bit integer rotation. The & ((1 << bits) - 1) part ensures that the result remains within the 32-bit range.

Use Cases

Bit rotation is used in various applications, including:

  • Cryptography: Used in encryption algorithms like block ciphers.
  • Data Compression: Can be used in some data compression techniques.
  • Hash Functions: Used in creating robust and distributed hash functions.
  • Error Detection/Correction: Can contribute to creating sophisticated detection and error correction algorithms.

Rotating bits involves shifting bits in a fixed-size data type, wrapping the bits that fall off one end to the other. This operation requires using bitwise shifts and OR operations, or leveraging built-in functions if available, while being mindful of the data type size and signedness.

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