Compound Bitwise Operators (&=, |=, ^=)

The compound bitwise operators perform their calculations at the bit level of variables. They are often used to clear and set specific bits of a variable.

See the bitwise math tutorial for more information on bitwise operators.

Compound bitwise AND (&=)

The compound bitwise AND operator &= is often used with a variable and a constant to force particular bits in a variable to be zero. This is often referred to in programming guides as “clearing” or “resetting” bits. In a program, writing the line x &= y; is equivalent to writing x = x & y;. That is, the value of x after the line will be equal to its old value bitwise ANDed with the value of y:

x &= y;   // equivalent to x = x & y;

You can use any integer variable for x (i.e., any variable of type int, char, byte, long long, etc.). You can use either an integer variable or any integer value (like 3 or 0x20) for y.

Before doing an example of &=, let’s first review the Bitwise AND (&) operator:

0  0  1  1    operand1
0  1  0  1    operand2
----------
0  0  0  1    (operand1 & operand2) = result

As shown above, bits that are “bitwise ANDed” with 0 become 0, while bits that are “bitwise ANDed” with 1 are left unchanged. So, if b is a byte variable, then b & B00000000 equals zero, and b & B11111111 equals b.

Note

The above uses binary constants. The numbers are still the same value in other representations, they just might not be as easy to understand.

Normally, in C and C++ code, hexadecimal or octal are used when we’re interested in an integer’s bits, rather than its value as a number.

While hexadecimal and octal literals might be harder to understand at first, you should really take the time to learn them. They’re part of C, C++, and many other programming languages, while binary constants are available only for compatibility with Arduino.

Also, B00000000 is shown for clarity, but zero in any number format is zero.

So, to clear (set to zero) bits 0 and 1 of a one-byte variable, while leaving the rest of the variable’s bits unchanged, use the compound bitwise AND operator &= with the constant B11111100 (hexadecimal 0xFC):

1  0  1  0  1  0  1  0    variable
1  1  1  1  1  1  0  0    mask
----------------------
1  0  1  0  1  0  0  0
^^^^^^^^^^^^^^^^  ^^^^
   unchanged      cleared

Here is the same representation with the variable’s bits replaced with the symbol x

x  x  x  x  x  x  x  x    variable
1  1  1  1  1  1  0  0    mask
----------------------
x  x  x  x  x  x  0  0
^^^^^^^^^^^^^^^^  ^^^^
   unchanged       cleared

So, using a byte variable b, if we say:

b =  B10101010; // B10101010 == 0xAA
b &= B11111100; // B11111100 == 0xFC

then we will have

b == B10101000; // B10101000 == 0xA8

Compound bitwise OR (|=)

The compound bitwise OR operator |= is often used with a variable and a constant to “set” (set to 1) particular bits in a variable. In a program, writing the line x |= y; is equivalent to writing x = x | y;. That is, the value of x after the line will be equal to its old value bitwise ORed with the value of y:

x |= y;   // equivalent to x = x | y;

You can use any integer variable for x (i.e., any variable of type int, char, long long etc.). You can use either an integer variable or any integer value (like 3 or 0x20) for y. (This works the same way as compound bitwise AND, &=).

Before doing an example of |=, let’s first review the Bitwise OR (|) operator:

0  0  1  1    operand1
0  1  0  1    operand2
----------
0  1  1  1    (operand1 | operand2) = result

Bits that are “bitwise ORed” with 0 are unchanged, while bits that are “bitwise ORed” with 1 are set to 1. So if b is a byte variable, then b | B00000000 equals b, and b & B11111111 equals B11111111 (here we’ve used binary constants; see the note above).

So, to set bits 0 and 1 of a one-byte variable, while leaving the rest of the variable unchanged, use the compound bitwise OR operator (|=) with the constant B00000011 (hexadecimal 0x3):

1  0  1  0  1  0  1  0    variable
0  0  0  0  0  0  1  1    mask
----------------------
1  0  1  0  1  0  1  1
^^^^^^^^^^^^^^^^  ^^^^
    unchanged      set

Here is the same representation with the variable’s bits replaced with the symbol x:

x  x  x  x  x  x  x  x    variable
0  0  0  0  0  0  1  1    mask
----------------------
x  x  x  x  x  x  1  1
^^^^^^^^^^^^^^^^  ^^^^
    unchanged      set

So, using a byte variable b, if we say:

b  = B10101010; // B10101010 == 0xAA
b |= B00000011; // B00000011 == 0x3

then we will have

b == B10101011; // B10101011 == 0xAB

Compound bitwise XOR (^=)

The compound bitwise XOR operator ^= is used with a variable and a constant to “toggle” (change 0 to 1, and 1 to 0) particular bits in a variable. In a program, writing the line x ^= y; is equivalent to writing x = x ^ y;. That is, the value of x after the line will be equal to its old value bitwise XORed with the value of y:

x ^= y;   // equivalent to x = x ^ y;

You can use any integer variable for x (i.e., any variable of type int, char, long long, etc.). You can use either an integer variable or any integer value (like 3 or 0x20) for y. (This works the same way as &= and |=; in fact, these three operators all work the same in this way).

Before doing an example of ^=, let’s first review the Bitwise XOR operator, ^:

0  0  1  1    operand1
0  1  0  1    operand2
----------
0  1  1  0    (operand1 ^ operand2) = result

One way to look at bitwise XOR is that each bit in the result is a 1 if the input bits are different, or 0 if they are the same. Another way to think about it is that the result bit will be 1 when exactly one (no more, no less) of the input bits is 1; otherwise, it will be zero. This means that if you XOR a bit with 1, it will change (or toggle) its value, while if you XOR a bit with 0, it stays the same.

So, to toggle bits 0 and 1 of a one-byte variable, while leaving the rest of the variable unchanged, use the compound bitwise XOR operator ^= with the constant B00000011 (hexadecimal 0x3; see note above):

1  0  1  0  1  0  1  0    variable
0  0  0  0  0  0  1  1    mask
----------------------
1  0  1  0  1  0  1  1
^^^^^^^^^^^^^^^^  ^^^^
    unchanged     toggled

So, using a byte variable b, if we say:

b  = B10101010; // B10101010 == 0xAA
b ^= B00000011; // B00000011 == 0x3

then we will have

b == B10101001; // B10101001 == 0xA9

See Also

• Boolean operations (&&, ||)
• Bitwise operators (&, |, ^, ~)

License and Attribution

This documentation page was adapted from the Arduino Reference Documentation, which is released under a Creative Commons Attribution-ShareAlike 3.0 License.