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en:reference:language:bitwiseand [2017/04/07 10:03] (current)
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 +====== 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.
 +===== 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:
 +<code cpp>
 +    0  0  1  1    operand1
 +    0  1  0  1    operand2
 +    ----------
 +    0  0  0  1    (operand1 & operand2) - returned result
 +</​code>​
 +In Ocrobot, 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:
 +<code cpp>
 +    int a =  92;    // in binary: 0000000001011100
 +    int b = 101;    // in binary: 0000000001100101
 +    int c = a & b;  // result: ​   0000000001000100,​ or 68 in decimal.
 +</​code>​
 +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:
 +<code cpp>
 +    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:
 +<code cpp>
 +    int a =  92;    // in binary: 0000000001011100
 +    int b = 101;    // in binary: 0000000001100101
 +    int c = a | b;  // result: ​   0000000001111101,​ or 125 in decimal.
 +</​code>​
 +===== 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 Ocrobot 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).
 +<code cpp>
 +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);
 +   }
 +}
 +</​code>​
 +===== 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:
 +<code cpp>
 +    0  0  1  1    operand1
 +    0  1  0  1    operand2
 +    ----------
 +    0  1  1  0    (operand1 ^ operand2) - returned result
 +</​code>​
 +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:
 +<code cpp>
 +    int x = 12;     // binary: 1100
 +    int y = 10;     // binary: 1010
 +    int z = x ^ y;  // binary: 0110, or decimal 6
 +</​code>​
 +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.
 +<code cpp>
 +// 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);
 +}
 +</​code>​
 +
  
en/reference/language/bitwiseand.txt · Last modified: 2017/04/07 10:03 (external edit)