# Bit Shifting

A bit shift moves each digit in a number's binary representation left or right. There are three main types of shifts:

### Left Shifts

When shifting left, the most-significant bit is lost, and a 0 bit is inserted on the other end.

The left shift operator is usually written as "<<".

0010 << 1 → 0100 0010 << 2 → 1000

A single left shift multiplies a binary number by 2:

0010 << 1 → 0100 0010 is 2 0100 is 4

### Logical Right Shifts

When shifting right with a logical right shift, the least-significant bit is lost and a 0 is inserted on the other end.

1011 >> 1 → 0101 1011 >> 3 → 0001

For positive numbers, a single logical right shift divides a number by 2, throwing out any remainders.

0101 >> 1 → 0010 0101 is 5 0010 is 2

### Arithmetic Right Shifts

When shifting right with an arithmetic right shift, the least-significant bit is lost and the most-significant bit is copied.

Languages handle arithmetic and logical right shifting in different ways. Python's right shift operator (>>) always does arithmetic right shifting.

1011 >> 1 → 1101 1011 >> 3 → 1111 0011 >> 1 → 0001 0011 >> 2 → 0000

The first two numbers had a 1 as the most significant bit, so more 1's were inserted during the shift. The last two numbers had a 0 as the most significant bit, so the shift inserted more 0's.

If a number is encoded using two's complement, then an arithmetic right shift preserves the number's sign, while a logical right shift makes the number positive.

# Arithmetic shift 1011 >> 1 → 1101 1011 is -5 1101 is -3 # Logical shift # (Not a thing in Python, but if it were:) 1111 >> 1 → 0111 1111 is -1 0111 is 7