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 000 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 000 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 111 as the most significant bit, so more 111's were inserted during the shift. The last two numbers had a 000 as the most significant bit, so the shift inserted more 000'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
```