# Bit Operation

Posted on: March 16, 2009

In computer science, a mask is data that is used for bitwise operations.

Using a mask, multiple bits in a byte, nibble, word (etc.) can be set either on, off or inverted from on to off (or vice versa) in a single bitwise operation.

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##### Masking bits to `1`

To turn certain bits on, the bitwise `OR` operation can be used. Recall that `Y OR 1 = 1` and `Y OR 0 = Y`. Therefore, to make sure a bit is on, `OR` can be used with a `1`. To leave a bit unchanged, `OR` is used with a `0`.

Example – turning on the 5th bit

```    10011101   10010101
OR 00001000   00001000
= 10011101   10011101```

##### Masking bits to `0`

There is no way to change a bit from on to off using the `OR` operation. Instead, bitwise `AND` is used. When a value is `AND`ed with a `1`, the result is simply the original value, as in: `Y AND 1 = Y`. However, `AND`ing a value with `0` is guaranteed to return a`0`, so it is possible to turn a bit off by `AND`ing it with `0`: `Y AND 0 = 0`. To leave the other bits alone, `AND`ing them with a `1` can be done.

Example – Turning off the 5th bit

```    10011101   10010101
AND 11110111   11110111
= 10010101   10010101```

##### Querying the status of a bit

It is possible to use bitmasks to easily check the state of individual bits regardless of the other bits. To do this, turning off all the other bits using the bitwise `AND` is done as discussed above and the value is compared with `0`. If it is equal to `0`, then the bit was off, but if the value is any other value, then the bit was on. What makes this convenient is that it is not necessary to figure out what the value actually is, just that it is not `0`.

Example – Querying the status of the 5th bit

```    10011101   10010101
AND 00001000   00001000
= 00001000   00000000```

##### Toggling bit values

So far the article has covered how to turn bits on and turn bits off, but not both at once. Sometimes it does not really matter what the value is, but it must be made the opposite of what it currently is. This can be achieved using the `XOR` (exclusive or) operation. `XOR` returns `1` if and only if an odd number of bits are `1`. Therefore, if two corresponding bits are `1`, the result will be a `0`, but if only one of them is `1`, the result will be `1`. Therefore inversion of the values of bits is done by `XOR`ing them with a `1`. If the original bit was `1`, it returns `1 XOR 1 = 0`. If the original bit was `0` it returns `0 XOR 1 = 1`. Also note that `XOR` masking is bit-safe, meaning that it will not affect unmasked bits because `Y XOR 0 = Y`, just like an `OR`.

##### Arguments to functions

In programming languages such as C, bit masks are a useful way to pass a set of named boolean arguments to a function. For example, in the graphics API OpenGL, there is a command, `glClear()` which clears the screen or other buffers. It can clear up to four buffers (the color, depth, accumulation, and stencil buffers), so the API authors could have had it take four arguments. But then a call to it would look like

`glClear(1,1,0,0); // This is not how glClear actually works and would make for unreadable code.`

which is not very descriptive. Instead there are four defined field bits, `GL_COLOR_BUFFER_BIT`, `GL_DEPTH_BUFFER_BIT`, `GL_ACCUM_BUFFER_BIT`, and `GL_STENCIL_BUFFER_BIT` and `glClear()` is declared as

`void glClear(GLbitfield mask);`

Then a call to the function looks like this

`glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);`

Internally, a function taking a bitfield like this can use binary `and` to extract the individual bits. For example, an implementation of `glClear()` might look like:

```void glClear(GLbitfield mask) {
// Clear color buffer.
}
// Clear depth buffer.
}
// Clear accumulation buffer.
}
// Clear stencil buffer.
}
}```

The advantage to this approach is that function argument overhead is decreased. Since the minimum datum size is one byte, separating the options into separate arguments would be wasting seven bits per argument and would occupy more stack space. Instead, functions typically accept one or more 32-bit integers, with up to 32 option bits in each. While elegant, in the simplest implementation this solution is not type-safe. A `GLbitfield` is simply defined to be an `unsigned int`, so the compiler would allow a meaningless call to `glClear(42)` or even `glClear(GL_POINTS)`. In C++ an alternative would be to create a class to encapsulate the set of arguments that glClear could accept and could be cleanly encapsulated in a library (see the external links for an example).

network address (traffic that is to be processed) 10.1.1.0

Based on the binary mask, it can be seen that the first three sets (octets) must match the given binary network address exactly (00001010.00000001.00000001). The last set of numbers are "don’t cares" (.11111111). Therefore, all traffic that begins with 10.1.1. matches since the last octet is "don’t care". Therefore, with this mask, network addresses 10.1.1.1 through 10.1.1.255 (10.1.1.x) are processed.

Subtract the normal mask from 255.255.255.255 in order to determine the ACL inverse mask. In this example, the inverse mask is determined for network address 172.16.1.0 with a normal mask of 255.255.255.0.

ACL equivalents

The source/source-wildcard of 0.0.0.0/255.255.255.255 means "any".

The source/wildcard of 10.1.1.2/0.0.0.0 is the same as "host 10.1.1.2"

Raster graphicsprites (left) and masks (right)

In computer graphics, when a given image is intended to be placed over a background, the transparent areas can be specified through a binary mask. This way, for each intended image there are actually two bitmaps: the actual image, in which the unused areas are given a pixel value with all bits set to 0’s, and an additional mask, in which the correspondent image areas are given a pixel value of all bits set to 0’s and the surrounding areas a value of all bits set to 1’s. In the sample at right, black pixels have the all-zero bits and white pixels have the all-one bits.

At run time, to put the image on the screen over the background, the program first masks the screen pixel’s bits with the image mask at the desired coordinates using the bitwise AND operation. This preserves the background pixels of the transparent areas while resets with zeros the bits of the pixels which will be obscured by the overlapped image.

Then, the program renders the image pixel’s bits by blending them with the background pixel’s bits using the bitwise OR operation. This way, the image pixels are appropiately placed while keeping the background surrounding pixels preserved. The result is a perfect compound of the image over the background.

This technique is used for painting pointing device cursors, in typical 2-D videogames for characters, bullets and so on (the sprites), for GUI icons, and for video titling and other image mixing applications.

Although related (due to being used for the same purposes), transparent colors and alpha channels are techniques which do not involve the image pixel mixage by binary masking.

##### Hash tables

To create a hashing function for a hash table often a function is used that has a large domain. To create an index from the output of the function, a modulo can be taken to reduce the size of the domain to match the size of the array; however, it is often faster on many processors to restrict the size of the hash table to powers of two sizes and use a bit mask instead.