# Bit Shifting

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. Java provides two right shift operators: >> does an arithmetic right shift and >>> does a logical right shift.

  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
1111 >>> 1  →  0111
1111 is -1
0111 is  7

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