<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"> <html> <head> <title>Arduino - BitwiseAnd </title> <link rel='stylesheet' href='arduino.css' type='text/css' /> <meta name="verify-v1" content="TtxFIEJAB6zdJ509wLxjnapQzKAMNm9u0Wj4ho6wxIY=" /> </head> <body> <div id="page"> <!--PageHeaderFmt--> <div id="pageheader"> <div class="title"><a href="http://www.arduino.cc"/>Arduino</a></div> <div class="search"> <!-- SiteSearch Google --> <FORM method=GET action="http://www.google.com/search"> <input type=hidden name=ie value=UTF-8> <input type=hidden name=oe value=UTF-8> <INPUT TYPE=text name=q size=25 maxlength=255 value=""> <INPUT type=submit name=btnG VALUE="search"> <input type=hidden name=domains value="http://www.arduino.cc/"> <input type=hidden name=sitesearch value="http://www.arduino.cc/"> </FORM> <!-- SiteSearch Google --> </div> </div> <!--/PageHeaderFmt--> <!--PageLeftFmt--> <div id="pagenav" style="text-align: right"> <div style="float: left;"> <p><a class='wikilink' href='http://arduino.cc/en/Main/Buy'>Buy</a> | <a class='wikilink' href='http://arduino.cc/en/Main/Software'>Download</a> | <a class='wikilink' href='Guide_index.html'>Getting Started</a> | <a class='wikilink' href='http://arduino.cc/en/Tutorial/HomePage'>Learning</a> | <a class='wikilink' href='index.html'>Reference</a> | <a class='wikilink' href='http://arduino.cc/en/Main/Hardware'>Hardware</a> | <a class='wikilink' href='FAQ.html'>FAQ</a> </p> <p class='vspace'></p> </div> <a class="urllink" href="http://www.arduino.cc/blog/" rel="nofollow">Blog »</a> | <a class="urllink" href="http://www.arduino.cc/cgi-bin/yabb2/YaBB.pl" rel="nofollow">Forum »</a> | <a class="urllink" href="http://www.arduino.cc/playground/" rel="nofollow">Playground »</a> </div> <!--/PageLeftFmt--> <div id="pagetext"> <!--PageText--> <div id='wikitext'> <p><strong>Reference</strong> <a class='wikilink' href='index.html'>Language</a> (<a class='wikilink' href='Extended.html'>extended</a>) | <a class='wikilink' href='Libraries.html'>Libraries</a> | <a class='wikilink' href='Comparison.html'>Comparison</a> | <a class='wikilink' href='Changes.html'>Changes</a> </p> <p class='vspace'></p><h2>Bitwise AND (&), Bitwise OR (|), Bitwise XOR (^)</h2> <h4>Bitwise AND (&)</h4> <p>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 <a class='urllink' href='http://www.arduino.cc/playground/Code/BitMath' rel='nofollow'>here.</a> </p> <p class='vspace'></p><h4>Description and Syntax</h4> <p>Below are descriptions and syntax for all of the operators. Further details may be found in the referenced tutorial. </p> <p class='vspace'></p><h4>Bitwise AND (&)</h4> <p>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: </p> <p class='vspace'></p><pre> 0 0 1 1 operand1 0 1 0 1 operand2 ---------- 0 0 0 1 (operand1 & operand2) - returned result </pre> <p class='vspace'></p><p>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: </p> <p class='vspace'></p><pre> int a = 92; // in binary: 0000000001011100 int b = 101; // in binary: 0000000001100101 int c = a & b; // result: 0000000001000100, or 68 in decimal. </pre> <p class='vspace'></p><p>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. </p> <p class='vspace'></p><p>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 </p> <p class='vspace'></p><h4>Bitwise OR (|)</h4> <p>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: </p> <p class='vspace'></p><pre> 0 0 1 1 operand1 0 1 0 1 operand2 ---------- 0 1 1 1 (operand1 | operand2) - returned result </pre> <p class='vspace'></p><p>Here is an example of the bitwise OR used in a snippet of C++ code: </p> <p class='vspace'></p><pre> int a = 92; // in binary: 0000000001011100 int b = 101; // in binary: 0000000001100101 int c = a | b; // result: 0000000001111101, or 125 in decimal. </pre> <p class='vspace'></p><h4>Example Program</h4> <p>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. </p> <p class='vspace'></p><p>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 <code>PORTD = B00110001;</code> we have made pins 2,3 & 7 HIGH. One slight hitch here is that we <em>may</em> 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. </p> <p class='vspace'></p><pre> Our algorithm for the program is: </pre><ul><li>Get PORTD and clear out only the bits corresponding to the pins we wish to control (with bitwise AND). </li><li>Combine the modified PORTD value with the new value for the pins under control (with biwise OR). </li></ul><p class='vspace'></p><pre>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); } } </pre> <p class='vspace'></p><h4>Bitwise XOR (^)</h4> <p>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: </p> <p class='vspace'></p><pre> 0 0 1 1 operand1 0 1 0 1 operand2 ---------- 0 1 1 0 (operand1 ^ operand2) - returned result </pre> <p class='vspace'></p><p>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. </p> <p class='vspace'></p><p>Here is a simple code example: </p> <p class='vspace'></p><pre> int x = 12; // binary: 1100 int y = 10; // binary: 1010 int z = x ^ y; // binary: 0110, or decimal 6 </pre> <p class='vspace'></p><p>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. </p> <p class='vspace'></p><pre> // 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); } </pre> <p class='vspace'></p><p>See Also </p><ul><li><a class='wikilink' href='Boolean.html'>&&</a>(Boolean AND) </li><li><a class='wikilink' href='Boolean.html'>||</a>(Boolean OR) </li></ul><p class='vspace'></p><p><a class='wikilink' href='index.html'>Reference Home</a> </p> <p class='vspace'></p><p><em>Corrections, suggestions, and new documentation should be posted to the <a class='urllink' href='http://www.arduino.cc/cgi-bin/yabb2/YaBB.pl?board=swbugs' rel='nofollow'>Forum</a>.</em> </p> <p class='vspace'></p><p>The text of the Arduino reference is licensed under a <a class='urllink' href='http://creativecommons.org/licenses/by-sa/3.0/' rel='nofollow'>Creative Commons Attribution-ShareAlike 3.0 License</a>. 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