Bitwise operators in Java

Bitwise operators operate on its operands in a bit-by-bit pattern. These operators only accept operands of integral types, including byte, char, short, int, long.

Operators OR, AND, and XOR

Before performing these operators &, |, ^, binary numeric promotion is applied on the operands [2]. If one of the operands is of type long, the other is promoted to long; otherwise, both operands are converted to int. The type of those operator expressons is the promoted type.

It should also be noticed that when these operators &, |, ^ are used on boolean values, they are called logical operators [2], and that short-circuiting is not supported in this case.

OR

Rule: x | y == 1 if x or y is 1.

Example:

0b1010111 | 0b1000010 == 0b1010111

AND

Rule: x & y == 1 if both x and y are 1.

Example:

0b1010111 & 0b1000010 == 0b1000010

XOR

Rule: x ^ y == 1 if either x or y is 1 but not both.

Example:

0b1010111 ^ 0b1000010 == 0b10101

Complement operator

The result of ~ x is obtained by flipping all the bits in x.

Example:

~ 0b1010111 == 0b11111111111111111111111110101000

Note that unary numeric promotion is applied before this operator is performed. If the operand is of type long, it remains unchanged; otherwise, it is converted to int. This promoted type is also the type of the result.

Shift operators

Before performing these operators, unary numeric promotion is applied on each operand. As stated before, in unary numeric promotion, an operand remains unchanged if its type if long, otherwise it is converted to int. The type of these shift expressions is the promoted type of the left operand.

Left shift

The result of x << y is x after shifting its bits y positions to the left and then inserting zeroes at the lower-order bits.

Example:

0b1010111 << 3 == 0b1010111000

Signed right shift

The result of x >> y is x after shifting its bits y positions to the right and then inserting at the higher-order bits zeroes if x > 0 or ones if x < 0.

Example:

// 0b10101 = 21
0b10101 >> 3 == 0b10
// 0b11111111111111111111111110011011 = -101
0b11111111111111111111111110011011 >> 3 == 0b11111111111111111111111111110011

Unsigned right shift

Same as >> except that the inserted bits are always zeroes.

Example:

0b11111111111111111111111110011011 >>> 3 == 0b00011111111111111111111111110011

Idioms

Let n denote an integer, and b denote the ith bit in n couting from the LSB.

• Clear all but b: n & (1 << i)

0b11111 & (1 << 2) == 0b00100

• Turn b off: n & (~ (1 << i))

0b1111 & (~(1 << 2)) == 0b11011

• Turn b on: n | (1 << i)

0b11000 | (1 << 2) == 0b11100

• Set b to bit a: (n & (~ (1 << i))) | (a << i)

0b11111 & ((~ (1 << 2)) | (0 << 2)) == 0b11011
0b11011 & ((~ (1 << 2)) | (1 << 2)) == 0b11111

• Create a bit mask with i trailing ones: (1 << i) - 1

(1 << 5) - 1 == 0b11111
(1 << 10) - 1 == 0b1111111111

• Clear the right most bit 1: n & (n - 1)

0b111011_1 & (0b111011_1 - 1) == 0b111011_0
0b11101_100 & (0b11101_100 -1) == 0b11101_000
0b1_000000 & (0b1_000000 - 1) == 0

Further reading

[1] Bitwise operators, Thinking in Java, 4th

[2] Bitwise and logical operators