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diff --git a/source/arduino/bitwiseand.rst b/source/arduino/bitwiseand.rst new file mode 100644 index 0000000..8d4eb3f --- /dev/null +++ b/source/arduino/bitwiseand.rst @@ -0,0 +1,230 @@ +.. _arduino-bitwiseand: + +Bitwise AND (&), Bitwise OR (\|), Bitwise XOR (^) +================================================= + +Bitwise AND (&) +--------------- + +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 below is from an excellent tutorial +on bitwise math wihch may be found +`here. <http://www.arduino.cc/playground/Code/BitMath>`_ + + + +Description and Syntax +---------------------- + +Below are descriptions and syntax for all of the operators. Further +details may be found in the referenced tutorial. + + + +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) - returned result + + + +In Arduino, the type int is a 16-bit value, so using & between two +int expressions causes 16 simultaneous AND operations to occur. In +a code fragment like: + + + +:: + + int a = 92; // in binary: 0000000001011100 + int b = 101; // in binary: 0000000001100101 + int c = a & b; // result: 0000000001000100, or 68 in decimal. + + + +Each of the 16 bits in a and b are processed by using the bitwise +AND, and all 16 resulting bits are stored in c, resulting in the +value 01000100 in binary, which is 68 in decimal. + + + +One of the most common uses of bitwise AND is to select a +particular bit (or bits) from an integer value, often called +masking. See below for an example + + + +Bitwise OR (\|) +--------------- + +The bitwise OR operator in C++ is the vertical bar symbol, \|. Like +the & operator, \| operates independently each bit in its two +surrounding integer expressions, but what it does is different (of +course). The bitwise OR of two bits is 1 if either or both of the +input bits is 1, otherwise it is 0. In other words: + + + +:: + + 0 0 1 1 operand1 + 0 1 0 1 operand2 + ---------- + 0 1 1 1 (operand1 | operand2) - returned result + + + +Here is an example of the bitwise OR used in a snippet of C++ +code: + + + +:: + + int a = 92; // in binary: 0000000001011100 + int b = 101; // in binary: 0000000001100101 + int c = a | b; // result: 0000000001111101, or 125 in decimal. + + + +Example Program +--------------- + +A common job for the bitwise AND and OR operators is what +programmers call Read-Modify-Write on a port. On microcontrollers, +a port is an 8 bit number that represents something about the +condition of the pins. Writing to a port controls all of the pins +at once. + + + +PORTD is a built-in constant that refers to the output states of +digital pins 0,1,2,3,4,5,6,7. If there is 1 in an bit position, +then that pin is HIGH. (The pins already need to be set to outputs +with the pinMode() command.) So if we write ``PORTD = B00110001;`` +we have made pins 2,3 & 7 HIGH. One slight hitch here is that we +*may* also have changeed the state of Pins 0 & 1, which are used by +the Arduino for serial communications so we may have interfered +with serial communication. + + + +:: + + Our algorithm for the program is: + + +- Get PORTD and clear out only the bits corresponding to the pins + we wish to control (with bitwise AND). +- Combine the modified PORTD value with the new value for the pins + under control (with biwise OR). + + + +:: + + int i; // counter variable + int j; + + void setup(){ + DDRD = DDRD | B11111100; // set direction bits for pins 2 to 7, leave 0 and 1 untouched (xx | 00 == xx) + // same as pinMode(pin, OUTPUT) for pins 2 to 7 + Serial.begin(9600); + } + + void loop(){ + for (i=0; i<64; i++){ + + PORTD = PORTD & B00000011; // clear out bits 2 - 7, leave pins 0 and 1 untouched (xx & 11 == xx) + j = (i << 2); // shift variable up to pins 2 - 7 - to avoid pins 0 and 1 + PORTD = PORTD | j; // combine the port information with the new information for LED pins + Serial.println(PORTD, BIN); // debug to show masking + delay(100); + } + } + + + +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 "eks-or".) The bitwise XOR operator is written +using the caret symbol ^. This operator is very similar to the +bitwise OR operator \|, only 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) - returned 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 code example: + + + +:: + + int x = 12; // binary: 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 5. + + + +:: + + // Blink_Pin_5 + // demo for Exclusive OR + void setup(){ + DDRD = DDRD | B00100000; // set digital pin five as OUTPUT + Serial.begin(9600); + } + + void loop(){ + PORTD = PORTD ^ B00100000; // invert bit 5 (digital pin 5), leave others untouched + delay(100); + } + + + +See Also + + +- `&& <http://arduino.cc/en/Reference/Boolean>`_ (Boolean AND) +- `\|\| <http://arduino.cc/en/Reference/Boolean>`_ (Boolean OR) + |