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The >> operator is the bitwise right shift operator. It shifts the binary representation of an integer to the right by a specified number of bit positions. Because Python integers have arbitrary precision and are conceptually represented using an infinite-width two’s complement format, the >> operator performs an arithmetic right shift, meaning it preserves the sign bit via sign extension.

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Syntax

result = x >> y
  • x (Left Operand): The integer whose bits will be shifted.
  • y (Right Operand): The number of bit positions to shift x to the right. This must be a non-negative integer.

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Mathematical Equivalence

The operation x >> y is strictly equivalent to the floor division of x by 2y2^y. 
x >> y == x // (2 ** y)

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Mechanical Behavior

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1. Positive Integers

When shifting a positive integer, the rightmost y bits are discarded, and y number of 0 bits are conceptually shifted in from the left. 
x = 22      # Binary: ...0001 0110
y = 2
    
result = x >> y  # Binary: ...0000 0101 (Decimal: 5)

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2. Negative Integers

When shifting a negative integer, Python maintains the two’s complement sign. The rightmost y bits are discarded, and y number of 1 bits are shifted in from the left to preserve the negative value. Because the operation equates to floor division, shifting a negative number rounds towards negative infinity. 
x = -22     # Binary: ...1110 1010
y = 2
    
result = x >> y  # Binary: ...1111 1010 (Decimal: -6)

# Mathematical equivalent: -22 // (2 ** 2) == -22 // 4 == -6

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3. Invalid Operands

The right operand (y) must be greater than or equal to zero. Attempting to shift by a negative number results in a ValueError. 
x = 10
result = x >> -1  # Raises ValueError: negative shift count
If either operand is not an integer, Python will attempt to invoke the __rshift__ (on the left operand) or __rrshift__ (on the right operand) dunder methods. If the types do not implement these methods for the given operands, Python raises a TypeError.
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