Bit Shifting: Left Shift and Right Shift Operations

Bit shifting moves all bits in a binary number to the left or right by a specified number of positions. It is one of the fastest operations a CPU can perform and is foundational to efficient algorithms.

Left shift (<<):

Shifts bits to the left, filling vacated positions with zeros. Each left shift multiplies the value by 2.

00001010 << 1 = 00010100  (10 x 2 = 20)
00001010 << 3 = 01010000  (10 x 8 = 80)

Right shift (>>):

Shifts bits to the right. Each right shift divides by 2 (integer division, truncating the remainder).

00010100 >> 1 = 00001010  (20 / 2 = 10)
00010100 >> 2 = 00000101  (20 / 4 = 5)

Logical vs. arithmetic right shift:

• Logical shift (>>> in JavaScript): Fills with zeros. Used for unsigned numbers.
• Arithmetic shift (>>): Fills with the sign bit (preserves negative numbers). 11110000 >> 2 = 11111100 (the leading 1s are preserved).

Performance advantage:

Shifting is much faster than multiplication/division on most CPUs. Multiplying by powers of 2 via shifting is a classic optimization:

• n * 4 = n << 2
• n / 8 = n >> 3
• n * 10 = (n << 3) + (n << 1)

Practical applications:

• Color channel extraction: (pixel >> 8) & 0xFF extracts the green channel from a 24-bit RGB value.
• Power of 2 calculation: 1 << n computes 2 raised to the power n.
• Bit field packing: Combine multiple small values into one integer by shifting and OR-ing.
• Fast averaging: (a + b) >> 1 computes the average of two integers (be careful of overflow).

Common pitfalls:

• Shifting by more than the bit width is undefined behavior in C/C++.
• Shifting negative numbers with >> is implementation-defined in C (though virtually all modern compilers use arithmetic shift).
• In JavaScript, all bitwise operations work on 32-bit integers, even though numbers are 64-bit floats.