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 "<<".
python
0010 << 1 → 0100
0010 << 2 → 1000
A single left shift multiplies a binary number by 2:
python
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.
python
1011 >> 1 → 0101
1011 >> 3 → 0001
For positive numbers, a single logical right shift divides a number by 2, throwing out any remainders.
python
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.
python
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.
python
# 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