Bit Shifting

Shifting moves the bits of a value left or right, multiplying or dividing by powers of two.

Left shift

A left shift by k moves every bit k places toward the high end, filling the low bits with zeros. For values that do not overflow, this multiplies by 2ᵏ: 3 << 2 equals 12.

Right shift

Kronos motion — number counters

A right shift by k moves bits toward the low end. For unsigned values it fills the high bits with zeros and divides by 2ᵏ, discarding any remainder. So 13 >> 1 equals 6.

Logical versus arithmetic right shift

For signed values, an arithmetic right shift copies the sign bit into the vacated high bits, preserving the sign; a logical shift fills with zeros. Languages differ in which they apply, so signed right shifts need care.

Uses

Fast multiply or divide by powers of two
Packing several fields into one integer
Extracting a bit range with shift then mask
Building bit masks such as 1 << n

Cautions

Shifting by a count greater than or equal to the word width is undefined or platform-dependent in many languages. Left-shifting into or past the sign bit can also cause overflow or unexpected sign changes.

python

print(3 << 2)   # 12
print(13 >> 1)  # 6
print((-8) >> 1)  # -4 in Python (arithmetic)