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+.. highlight:: cpp
+
+.. _lang-bitwisemath:
+
+Bitwise Operators (``&``, ``|``, ``^``, ``~``)
+==============================================
+
+The bitwise operators perform their calculations at the bit level of
+variables. They help solve a wide range of common programming
+problems.
+
+Much of the material here is adapted for Maple from an (Arduino)
+`tutorial on bitwise math
+<http://www.arduino.cc/playground/Code/BitMath>`_\ .  Another great
+resource is the Wikipedia article on `bitwise operations
+<http://en.wikipedia.org/wiki/Bitwise_operation>`_\ .
+
+Below are descriptions and syntax for all of the operators.
+
+.. contents:: Contents
+   :local:
+
+.. _lang-bitwisemath-and:
+
+Bitwise AND (``&``)
+-------------------
+
+The bitwise AND operator in C++ is a single ampersand, ``&``, used
+between two other integer expressions. Bitwise AND operates on each
+bit position of the surrounding expressions independently, according
+to this rule: if both input bits are 1, the resulting output is 1,
+otherwise the output is 0. Another way of expressing this is::
+
+        0  0  1  1    operand1
+        0  1  0  1    operand2
+        ----------
+        0  0  0  1    (operand1 & operand2) = result
+
+
+On the Maple, the type ``int`` is a 32-bit value, so using ``&``
+between two ``int`` expressions causes 32 simultaneous AND operations
+to occur. In a code fragment like::
+
+        int a =  92;    // in binary: 00000000000000000000000001011100
+        int b = 101;    // in binary: 00000000000000000000000001100101
+        int c = a & b;  // result:    00000000000000000000000001000100,
+                        //    (or 68 in decimal).
+
+
+Each of the 32 bits in ``a`` and ``b`` are processed using bitwise
+AND, and all 32 resulting bits are stored in ``c``, resulting in the
+value 1000100 in binary, which is 68 in decimal.
+
+
+.. _lang-bitwisemath-or:
+
+Bitwise OR (``|``)
+------------------
+
+The bitwise OR operator in C++ is the vertical bar symbol, ``|``. Like
+the ``&`` operator, ``|`` operates independently on each bit in its
+two surrounding integer expressions, but what it does is
+different. The bitwise OR of two bits is 1 if either or both of the
+input bits is 1, otherwise it is 0.  For example::
+
+        0  0  1  1    operand1
+        0  1  0  1    operand2
+        ----------
+        0  1  1  1    (operand1 | operand2) = result
+
+Here is an example of bitwise OR used in a snippet of C++ code (using
+``char``, which takes up 8 bits of memory, instead of ``int``, which
+uses 32)::
+
+        char a =  92;    // in binary: 01011100
+        char b = 101;    // in binary: 01100101
+        char c = a | b;  // result:    01111101, or 125 in decimal.
+
+.. _lang-bitwisemath-xor:
+
+Bitwise XOR (``^``)
+-------------------
+
+There is a somewhat unusual operator in C++ called bitwise EXCLUSIVE
+OR, also known as bitwise XOR. (In English, this is usually pronounced
+"zor" or "ex-or"). The bitwise XOR operator is written using the caret
+symbol, ``^``. This operator is very similar to the bitwise OR
+operator ``|``, except it evaluates to 0 for a given bit position when
+both of the input bits for that position are 1::
+
+        0  0  1  1    operand1
+        0  1  0  1    operand2
+        ----------
+        0  1  1  0    (operand1 ^ operand2) = result
+
+
+Another 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.
+
+Here is a simple example::
+
+        int x = 12;     // binary (ignoring extra bits): 1100
+        int y = 10;     // binary:                       1010
+        int z = x ^ y;  // binary:                       0110, or decimal 6
+
+
+
+The ^ operator is often used to toggle (i.e. change from 0 to 1, or 1
+to 0) some of the bits in an integer expression. In a bitwise OR
+operation if there is a 1 in the mask bit, that bit is inverted; if
+there is a 0, the bit is not inverted and stays the same. Below is a
+program to blink digital pin 13 (the LED pin on Maple)::
+
+    // Blink Maple LED pin
+
+    int led_pin = 13;
+    int toggle = 0;
+
+    // demo for Exclusive OR
+    void setup(){
+        pinMode(led_pin, OUTPUT);
+    }
+
+    void loop(){
+        toggle = toggle ^ 1;
+        digitalWrite(led_pin, toggle);
+        delay(100);
+    }
+
+.. _lang-bitwisemath-not:
+
+Bitwise NOT (``~``)
+-------------------
+
+The bitwise NOT operator in C++ is the tilde character ``~``. Unlike
+``&`` and ``|``, the bitwise NOT operator is applied to a single
+operand to its right. Bitwise NOT changes each bit to its opposite: 0
+becomes 1, and 1 becomes 0. For example::
+
+        0  1    operand1
+        ----
+        1  0   ~operand1 = result
+
+Another example::
+
+        char a = 103;    // binary:  01100111
+        char b = ~a;     // binary:  10011000 = -104
+
+You might be surprised to see a negative number like -104 as the
+result of this operation. This is because the highest bit in an int
+variable is the so-called "sign bit". If the highest bit is 1, the
+number is interpreted as negative. This encoding of positive and
+negative numbers is referred to as *two's complement*. For more
+information, see the Wikipedia article on `two's
+complement. <http://en.wikipedia.org/wiki/Twos_complement>`_
+
+As an aside, it is interesting to note that (under two's complement
+arithmetic) for any integer ``x``, ``~x`` is the same as ``-x-1``.
+
+At times, the sign bit in a signed integer expression can cause
+some unwanted surprises.
+
+
+Uses
+----
+
+One of the most common uses of bitwise operations is to select or
+manipulate a particular bit (or bits) from an integer value, often
+called `bit masking
+<http://en.wikipedia.org/wiki/Mask_%28computing%29>`_\ . See the
+linked Wikipedia article for more information and examples.
+
+If you really want to see bit-twiddling techniques in their full
+glory, you could do much worse than to get yourself a copy of
+`Hacker's Delight <http://www.hackersdelight.org/>`_\ .
+
+
+See Also
+--------
+
+- :ref:`Boolean operations <lang-boolean>` (``&&``, ``||``)
+- :ref:`Compound bitwise operations <lang-compoundbitwise>` (``&=``,
+   ``|=``, ``^=``).
+
+
+.. include:: cc-attribution.txt