Right Shift as Divide by 2

Right Shift (>>) as Division

Shifting a binary number right by one position is equivalent to integer division by 2. Shifting right by N positions divides by 2^N (with truncation toward negative infinity for signed values).

How It Works

  40      = 00101000
  40 >> 1 = 00010100  (20, which is 40 / 2)
  40 >> 2 = 00001010  (10, which is 40 / 4)
  40 >> 3 = 00000101  ( 5, which is 40 / 8)

Each shift removes the rightmost bit and moves all bits one position to the right. For positive numbers, the vacated high bit is filled with 0.

Arithmetic vs. Logical Right Shift

• >> (arithmetic): Fills the vacated high bits with the sign bit. Negative numbers remain negative.
• >>> (logical, unsigned): Always fills with 0. Negative numbers become large positive numbers.

  -8 (signed 8-bit) = 11111000
  -8 >> 1            = 11111100  (-4, sign preserved)
  -8 >>> 1 (32-bit)  = 01111...1100  (2147483644)

Rounding Behavior

For positive numbers, >> truncates toward zero (same as Math.floor(n/2)). For negative numbers, it truncates toward negative infinity:

• -7 >> 1 = -4 (not -3)
• Math.floor(-7 / 2) = -4 (matches)
• Math.trunc(-7 / 2) = -3 (different!)

When to Use Each

Use >> when working with signed integers where you want to preserve the sign. Use >>> when treating the value as unsigned (e.g., hash functions, color channels).