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diff --git a/docs/source/lang/bitwisecompound.rst b/docs/source/lang/bitwisecompound.rst new file mode 100644 index 0000000..2b0fe2f --- /dev/null +++ b/docs/source/lang/bitwisecompound.rst @@ -0,0 +1,231 @@ +.. highlight:: cpp + +.. _lang-bitwisecompound: + +Compound bitwise and (&=), or (\|=), XOR (^=) +============================================= + +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 :ref:`bitwise math tutorial <lang-bitwisemath>` for more +information on bitwise operators. + +.. contents:: Contents + :local: + +.. _lang-bitwisecompound-and: + +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``, ``long``, ``char``, ``byte``, etc.). You can use either an +integer variable or any :ref:`integer value +<lang-constants-integers>` (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``. + +.. _lang-bitwisecompound-binconst: + +.. note:: The above uses :ref:`binary constants + <lang-constants-integers-bin>`\ . 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, :ref:`hexadecimal + <lang-constants-integers-hex>` or :ref:`octal + <lang-constants-integers-oct>` 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 + +.. _lang-bitwisecompound-or: + +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``, ``long``, ``char``, ``byte``, etc.). You can use either an +integer variable or any integer value (like ``3`` or ``0x20``) for +``y``. (This works the same way as :ref:`compound bitwise AND +<lang-bitwisecompound-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 +:ref:`note <lang-bitwisecompound-binconst>` 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 + +.. _lang-bitwisecompound-xor: + +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``, ``long``, ``char``, ``byte``, etc.). You can use either an +integer variable or any integer value (like ``3`` or ``0x20``) for +``y``. (This works the same way as :ref:`&= +<lang-bitwisecompound-and>` and :ref:`\|= +<lang-bitwisecompound-or>`; 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 +:ref:`note <lang-bitwisecompound-binconst>` 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 +-------- + +- :ref:`Boolean operations <lang-boolean>` (``&&``, ``||``) +- :ref:`Bitwise operators <lang-bitwisemath>` (``&``, ``|``, ``^``, ``~``) + + +.. include:: cc-attribution.txt |