## Reference.BitwiseAnd History

January 04, 2016, at 10:08 AM by Martino Facchin -
Changed lines 5-6 from:

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.

to:

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 which may be found here.

June 10, 2007, at 08:15 PM by Paul Badger -
Changed lines 80-81 from:

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:

to:

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:

June 10, 2007, at 08:12 PM by Paul Badger -
Changed lines 95-96 from:

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 NOR 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.

to:

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.

April 24, 2007, at 12:30 AM by Paul Badger -
Deleted line 106:

// all others unchanged

April 24, 2007, at 12:29 AM by Paul Badger -
Deleted line 99:
Changed line 106 from:

PORTD = PORTD & B00100000; // invert bit 5 (digital pin 5)

to:

PORTD = PORTD ^ B00100000; // invert bit 5 (digital pin 5), leave others untouched

Deleted line 108:
```   }
```
April 24, 2007, at 12:26 AM by Paul Badger -
Changed line 61 from:

DDRD = DDRD | 11111100; // set direction bits for pins 2 to 7, leave 0 and 1 untouched (xx | 00 == xx)

to:

DDRD = DDRD | B11111100; // set direction bits for pins 2 to 7, leave 0 and 1 untouched (xx | 00 == xx)

Changed lines 95-98 from:

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 NOR 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. For example:

```    y = x ^ B00000001;   // toggle the lowest bit in x, and store the result in y.
```
to:

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 NOR 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)
// all others unchanged
delay(100);
}
}
```

April 24, 2007, at 12:16 AM by Paul Badger -
Changed line 61 from:

DDRD = DDRD | 11111100; // set direction bits for pins 2 to 7, leave 0 & 1 untouched (xx | 00 == xx)

to:

DDRD = DDRD | 11111100; // set direction bits for pins 2 to 7, leave 0 and 1 untouched (xx | 00 == xx)

Deleted line 63:

Serial.println("start");

Changed lines 69-70 from:

PORTD = PORTD & B00000011; // clear out bits 2 - 7, leave pins 0 & 1 untouched (xx & 11 == xx) j = (i << 2); // shift variable up to pins 2 - 7 - to avoid pins 0 & 1

to:

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

April 24, 2007, at 12:14 AM by Paul Badger -
Changed lines 57-62 from:

[@// program to demonstrate writing to ports & bitmasking // Paul Badger 2007 // set some LED's (w. series resistors) up on pins 2 to 7 // and watch the program count in binary

int i; // counter variable

to:

[@int i; // counter variable

Changed line 61 from:

DDRD = DDRD & 11111100; // set direction bits for pins 2 to 7

to:

DDRD = DDRD | 11111100; // set direction bits for pins 2 to 7, leave 0 & 1 untouched (xx | 00 == xx)

Serial.begin(9600); Serial.println("start");

Changed line 67 from:

void loop{

to:

void loop(){

Changed lines 70-72 from:

PORTD = PORTD & B00000011; // mask out bits 2 - 7

to:

PORTD = PORTD & B00000011; // clear out bits 2 - 7, leave pins 0 & 1 untouched (xx & 11 == xx) j = (i << 2); // shift variable up to pins 2 - 7 - to avoid pins 0 & 1 PORTD = PORTD | j; // combine the port information with the new information for LED pins

Changed lines 74-76 from:

j = (i << 2); // shift variable up to pins 2 - 7 PORTD = PORTD | j; // combine the port information with the new information for LED pins Serial.println(PORTD, BIN); // debug to show masking

to:

delay(100);

Changed lines 76-78 from:

} @]

to:

}@]

April 18, 2007, at 03:47 PM by Paul Badger -
Changed lines 99-100 from:

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 NOR operation if there is 1 in the mask bit, that bit is inverted; if there is a 0, the bit is not inverted and stays the same. For example:

to:

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 NOR 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. For example:

April 18, 2007, at 03:43 PM by Paul Badger -
Changed line 15 from:
```    1  1  0  0    operand1
```
to:
```    0  0  1  1    operand1
```
Changed lines 18-19 from:
```    0  1  0  0    (operand1 & operand2) - returned result
```
to:
```    0  0  0  1    (operand1 & operand2) - returned result
```
Changed line 35 from:
```    1  1  0  0    operand1
```
to:
```    0  0  1  1    operand1
```
Changed lines 38-39 from:
```    1  1  0  1    (operand1 | operand2) - returned result
```
to:
```    0  1  1  1    (operand1 | operand2) - returned result
```
Changed line 86 from:
```    1  1  0  0    operand1
```
to:
```    0  0  1  1    operand1
```
Changed lines 89-90 from:
```    1  0  0  1    (operand1 ^ operand2) - returned result
```
to:
```    0  1  1  0    (operand1 ^ operand2) - returned result
```
April 18, 2007, at 03:40 PM by Paul Badger -
Changed lines 1-2 from:

to:

## Bitwise AND (&), Bitwise OR (|), Bitwise XOR (^)

Changed lines 99-100 from:

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 NOR operation if there is 1 in the mask bit, that bit is inverted, if there is a 0, the bit is not inverted and stays the same. For example:

to:

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 NOR operation if there is 1 in the mask bit, that bit is inverted; if there is a 0, the bit is not inverted and stays the same. For example:

April 18, 2007, at 03:35 PM by Paul Badger -

#### 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:

```    1  1  0  0    operand1
0  1  0  1    operand2
----------
1  0  0  1    (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 NOR operation if there is 1 in the mask bit, that bit is inverted, if there is a 0, the bit is not inverted and stays the same. For example:

```    y = x ^ B00000001;   // toggle the lowest bit in x, and store the result in y.
```
April 18, 2007, at 03:46 AM by Paul Badger -
Changed line 83 from:
• |(Boolean OR)
to:
• ||(Boolean OR)
April 18, 2007, at 03:46 AM by Paul Badger -
Changed lines 79-80 from:

}

to:

} @]

April 18, 2007, at 03:45 AM by Paul Badger -

#### Example Program

April 18, 2007, at 03:43 AM by Paul Badger -
Changed lines 80-81 from:
• &&?(Boolean AND)
• (Boolean OR)
to:
• &&(Boolean AND)
• |(Boolean OR)
April 18, 2007, at 03:41 AM by Paul Badger -
April 18, 2007, at 03:41 AM by Paul Badger -
Changed lines 80-81 from:

&&?(Boolean AND) (Boolean OR)

to:
• &&?(Boolean AND)
• (Boolean OR)
April 18, 2007, at 03:40 AM by Paul Badger -
Changed lines 1-2 from:

to:

## Bitwise AND (&), Bitwise OR (|)

#### Bitwise AND (&)

April 18, 2007, at 03:37 AM by Paul Badger -

## Bitwise AND (&), Bitwise OR (|), Bitwise XOR (^), Bitwise NOT (~)

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:

```    1  1  0  0    operand1
0  1  0  1    operand2
----------
0  1  0  0    (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:

```    1  1  0  0    operand1
0  1  0  1    operand2
----------
1  1  0  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.
```

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).

[@// program to demonstrate writing to ports & bitmasking // Paul Badger 2007 // set some LED's (w. series resistors) up on pins 2 to 7 // and watch the program count in binary

int i; // counter variable int j;

void setup(){ DDRD = DDRD & 11111100; // set direction bits for pins 2 to 7 // same as pinMode(pin, OUTPUT) for pins 2 to 7 }

void loop{ for (i=0; i<64; i++){

PORTD = PORTD & B00000011; // mask out bits 2 - 7 Serial.println(PORTD, BIN); // debug to show masking j = (i << 2); // shift variable up to pins 2 - 7 PORTD = PORTD | j; // combine the port information with the new information for LED pins Serial.println(PORTD, BIN); // debug to show masking

```   }
```

}