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O.3.8a — Bit flags and bit masks

Note: This is a tough lesson. If you find yourself stuck, you can safely skip this lesson and come back to it later.

Bit flags

The smallest addressable unit of memory is a byte. Since all variables need to have unique addresses, this means variables must be at least one byte in size.

For most variable types, this is fine. However, for boolean values, this is a bit wasteful. Boolean types only have two states: true (1), or false (0). This only requires one bit to store. However, if a variable must be at least a byte, and a byte is typically 8 bits, that means a boolean is using 1 bit and leaving the other 7 unused.

In the majority of cases, this is fine -- we’re usually not so hard-up for memory that we need to care about 7 wasted bits. However, in some storage-intensive cases, it can be useful to “pack” 8 individual boolean values into a single byte for storage efficiency purposes. This is done by using the bitwise operators to set, clear, and query individual bits in a byte, treating each as a separate boolean value. These individual bits are called bit flags.

Bit counting

When talking about individual bits, we typically count from right to left, starting with 0 (not 1). So given the bit pattern 0000 0111, bits 0 through 2 are 1, and bits 3 through 7 are 0.

So although we are typically used to counting starting with 1, in this lesson we’ll generally count starting from 0.

Defining bit flags in C++14

In order to work with individual bits, we need to have a way to identify the individual bits within a byte, so we can manipulate those bits (turn them on and off). This is typically done by defining a symbolic constant to give a meaningful name to each bit used. The symbolic constant is given a value that represents that bit.

Because C++14 supports binary literals, this is easiest in C++14:

Now we have a set of symbolic constants that represents each bit position. We can use these to manipulate the bits (which we’ll show how to do in just a moment).

Defining bit flags in C++11 or earlier

Because C++11 doesn’t support binary literals, we have to use other methods to set the symbolic constants. There are two good methods for doing this. Less comprehensible, but more common, is to use hexadecimal. If you need a refresher on hexadecimal, please revisit lesson 4.12 -- Literals.

This can be a little hard to read. One way to make it easier is to use the left-shift operator to shift a bit into the proper location:

Using bit flags to manipulate bits

The next thing we need is a variable that we want to manipulate. Typically, we use an unsigned integer of the appropriate size (8 bits, 16 bits, 32 bits, etc… depending on how many options we have).

Variable myflags, defined above, will hold the actual bits that we’ll turn on and off. How do we turns those bits on and off? We use our bit flags (options).

Turning individual bits on

To set a bit (turn on), we use bitwise OR equals (operator |=):

Let’s unpack this one to show how it works in more detail.

myflags |= option4 is the equivalent of myflags = (myflags | option4).

Evaluating the portion between the parenthesis:

myflags = 0000 0000 (we initialized this to 0)
option4 = 0001 0000
-------------------
result  = 0001 0000

So we get myflags = 0001 0000. In other words, we just turned the 4th bit on.

We can also turn on multiple bits at the same time using bitwise OR:

Turning individual bits off

To clear a bit (turn off), we use bitwise AND with an inverse bit pattern:

This works similarly to the above. Let’s say myflags was initially set to 0001 1100 (options 2, 3, and 4 turned on).

myflags &= ~option4; is the equivalent of myflags = (myflags & ~option4).

myflags  = 0001 1100
~option4 = 1110 1111
--------------------
result   = 0000 1100

So 0000 1100 gets assigned back to myflags. In other words, we just turned off bit 4 (and left the other bits alone).

We can turn off multiple bits at the same time:

Flipping individual bits

To toggle a bit state, we use bitwise XOR:

Determining if a bit is on or off

To query a bit state, we use bitwise AND:

Bit flags in real life

In OpenGL (a 3d graphics library), some functions take one or more bit flags as a parameter:

GL_COLOR_BUFFER_BIT and GL_DEPTH_BUFFER_BIT are defined as follows (in gl2.h):

Here’s a less abstract example for a game we might write:

Why are bit flags useful?

Astute readers will note that the above myflags example actually doesn’t save any memory. 8 booleans would normally take 8 bytes. But the above example uses 9 bytes (8 bytes to define the bit flag options, and 1 bytes for the bit flag)! So why would you actually want to use bit flags?

Bit flags are typically used in two cases:

1) When you have many sets of identical bitflags.

Instead of a single myflags variable, consider the case where you have two myflags variables: myflags1 and myflags2, each of which can store 8 options. If you defined these as two separate sets of booleans, you’d need 16 booleans, and thus 16 bytes. However, using bit flags, the memory cost is only 10 (8 bytes to define the options, and 1 byte for each myflags variable). With 100 myflag variables, your memory cost would be 108 bytes instead of 800. The more identical variables you need, the more substantial your memory savings.

Let’s take a look at a more concrete example. Imagine you’re creating a game where there are monsters for the player to fight. When a monster is created, it may be resistant to certain types of attacks (chosen at random). The different type of attacks in the game are: poison, lightning, fire, cold, theft, acid, paralysis, and blindness.

In order to track which types of attacks the monster is resistant to, we can use one boolean value per resistance (per monster). That’s 8 booleans per monster.

With 100 monsters, that would take 800 boolean variables, using 800 bytes of memory.

However, using bit flags:

Using bit flags, we only need one byte to store the resistances for a single monster, plus a one-time setup fee of 8 bytes for the options.

With 100 monsters, that would take 108 bytes total, or approximately 8 times less memory.

For most programs, the amount of memory using bit flags saved is not worth the added complexity. But in programs where there are tens of thousands or even millions of similar objects, using bit flags can reduce memory use substantially. It’s a useful optimization to have in your toolkit if you need it.

2) Imagine you had a function that could take any combination of 32 different options. One way to write that function would be to use 32 individual boolean parameters:

Hopefully you’d give your parameters more descriptive names, but the point here is to show you how obnoxiously long the parameter list is.

Then when you wanted to call the function with options 10 and 32 set to true, you’d have to do so like this:

This is ridiculously difficult to read (is that option 9, 10, or 11 that’s set to true?), and also means you have to remember which parameters corresponds to which option (is setting the edit flag the 9th, 10th, or 11th parameter?) It may also not be very performant, as every function call has to copy 32 booleans from the caller to the function.

Instead, if you defined the function using bit flags like this:

Then you could use bit flags to pass in only the options you wanted:

Not only is this much more readable, it’s likely to be more performant as well, since it only involves 2 operations (one bitwise OR and one parameter copy).

This is one of the reasons OpenGL opted to use bitflag parameters instead of many consecutive booleans.

Also, if you have unused bit flags and need to add options later, you can just define the bit flag. There’s no need to change the function prototype, which is good for backwards compatibility.

An introduction to std::bitset

All of this bit flipping is exhausting, isn’t it? Fortunately, the C++ standard library comes with functionality called std::bitset that helps us manage bit flags.

To create a std::bitset, you need to include the bitset header, and then define a std::bitset variable indicating how many bits are needed. The number of bits must be a compile time constant.

If desired, the bitset can be initialized with an initial set of values:

Note that our initialization value is interpreted as binary. Since we pass in the value 3, the std::bitset will start with the binary value for 3 (0000 0011).

std::bitset provides 4 key functions:

  • test() allows us to query whether a bit is a 0 or 1
  • set() allows us to turn a bit on (this will do nothing if the bit is already on)
  • reset() allows us to turn a bit off (this will do nothing if the bit is already off)
  • flip() allows us to flip a bit from a 0 to a 1 or vice versa

Each of these functions takes a bit-position parameter indicating which bit should be operated on. The position of the rightmost bit is 0, increasing with each successive bit to the left. Giving descriptive names to the bit indices can be useful here (either by assigning them to const variables, or using enums, which we’ll introduce in the next chapter).

This prints:

Bit 4 has value: 1
Bit 5 has value: 0
All the bits: 00010010

Note that sending the bitset variable to std::cout prints the value of all the bits in the bitset.

Remember that the initialization value for a bitset is treated as binary, whereas the bitset functions use bit positions!

std::bitset also supports the standard bit operators (operator|, operator&, and operator^), so you can still use those if you wish (they can be useful when setting or querying multiple bits at once).

We recommend using std::bitset instead of doing all the bit operations manually, as bitset is more convenient and less error prone.

(h/t to reader “Mr. D”)

Bit masks

The principles for bit flags can be extended to turn on, turn off, toggle, or query multiple bits at once, in a bit single operation. When we bundle individual bits together for the purpose of modifying them as a group, this is called a bit mask.

Let’s take a look at a sample program using bit masks. In the following program, we ask the user to enter a number. We then use a bit mask to keep only the low 4 bits, which we print the value of.

Enter an integer: 151
The 4 low bits have value: 7

151 is 1001 0111 in binary. lowMask is 0000 1111 in 8-bit binary. 1001 0111 & 0000 1111 = 0000 0111, which is 7 decimal.

Although this example is pretty contrived, the important thing to note is that we modified multiple bits in one operation!

An RGBA color example

Now lets take a look at a more complicated example.

Color display devices such as TVs and monitors are composed of millions of pixels, each of which can display a dot of color. The dot of color is composed from three beams of light: one red, one green, and one blue (RGB). By varying the intensity of the colors, any color on the color spectrum can be made. Typically, the amount of R, G, and B for a given pixel is represented by an 8-bit unsigned integer. For example, a red pixel would have R=255, G=0, B=0. A purple pixel would have R=255, G=0, B=255. A medium-grey pixel would have R=127, G=127, B=127.

When assigning color values to a pixel, in addition to R, G, and B, a 4th value called A is often used. “A” stands for “alpha”, and it controls how transparent the color is. If A=0, the color is fully transparent. If A=255, the color is opaque.

R, G, B, and A are normally stored as a single 32-bit integer, with 8 bits used for each component:

32-bit RGBA value
bits 31-24 bits 23-16 bits 15-8 bits 7-0
RRRRRRRR GGGGGGGG BBBBBBBB AAAAAAAA
red green blue alpha

The following program asks the user to enter a 32-bit hexadecimal value, and then extracts the 8-bit color values for R, G, B, and A.

This produces the output:

Enter a 32-bit RGBA color value in hexadecimal (e.g. FF7F3300): FF7F3300
Your color contains:
255 of 255 red
127 of 255 green
51 of 255 blue
0 of 255 alpha

In the above program, we use a bitwise AND to query the set of 8 bits we’re interested in, and then we right shift them to move them to the range of 0-255 for storage and printing.

Note: RGBA is sometimes stored as ARGB instead, with the alpha channel being stored in the most significant byte rather than the least significant.

Summary

Summarizing how to set, clear, toggle, and query bit flags:

To query bit states, we use bitwise AND:

To set bits (turn on), we use bitwise OR:

To clear bits (turn off), we use bitwise AND with an inverse bit pattern:

To toggle bit states, we use bitwise XOR:

Quiz

1) Given the following program:

1a) Write a line of code to set the article as viewed.
1b) Write a line of code to check if the article was deleted.
1c) Write a line of code to clear the article as a favorite.
1d) Extra credit: why are the following two lines identical?

Quiz answers

1a) Show Solution

1b) Show Solution

1c) Show Solution

1d) Show Solution

O.3.x -- Chapter O.3 comprehensive quiz
Index
O.3.8 -- Bitwise operators

254 comments to O.3.8a — Bit flags and bit masks

  • Vishal

    Hey Alex, I  learn C,  C++,  Java,  HTML,  CSS3,  javascript,  python.  I almost understand all programming concepts of these modern programming languages but until now I don't build any cool stuff. I don't know what to do when I learn some new language. Alex please give me some suggestions to how I make or create some great stuff and what should I do when  I learne some new programming language.

    • Hey Vishal, I've found this website (https://www.linuxtrainingacademy.com/projects/) particularly useful as a wellspring of ideas for things to try out when you learn a new programming language.  The links within suggest everything from simple manipulation programs to complex and massive projects, so I'm sure there will be something for every level of experience and comfort.  The projects are almost all language-agnostic too, so you might even challenge your skills by trying to code the same thing in many of the languages you mentioned.  Happy coding, and welcome to the community!

  • Grego

    Hello Alex & Nascardriver,

    This may be a stupid question, but why are contants in this lesson assigned to and not initialized?
    I looked back to char variables and constants lessons and could see both of them showing proper initialization.
    What makes this type of a constant not need an initialisation? Am I just missing something obvious?

    • Alex

      These lessons are still in the process of being rewritten/updated, so they aren't yet compliant with all modern best practices. The constants here are being initialized (not assigned) via copy initialization rather than the now-preferred uniform/brace initialization.

  • learning

    what's wrong with this code? gives a warning:

    • is an `int`, `red` is a `char`. Converting from `int` to `char` could cause data loss. You're doing it on purpose and know that you're not losing data. Add a cast to silence the warning.

  • Sagar Pohekar

    Hello,
    Thanks for the tutorial.
    BTW, you said you are in process of replacing compile time/symbolic constants from 'const' to 'constexpr', so this tutorial is good place to use 'constexpr'

    Thanks.

  • Alireza

    Hello and thank you so much for the Bit flags tutorial. This is very useful.

    question: Why have you used a char variable to use bit flags, Why haven't you used a bool variable or other ones to teach bit flags ?
    Does it mean especial ?

    Why the following program gives errors ?

    Imagine I write this program, which variable does bitset do ?

    • Alex

      std::bitset functions take bit positions, not bit masks. o1 works because it evaluates to bit 2, o2 works because it evaluates to bit 4, but o3 doesn't work because it evaluates to bit 8, which is out of range for a bitset of size 8.

      • Alireza

        Thanks for replying,
        So the inputed number in std::bitset as the size is not bits' number ; it is their values and must be equal to our flags.

        Sorry but you haven't answered it yet:

        Why have you used a char variable to use bit flags, Why haven't you used a bool variable or other ones to teach bit flags ?

        and one more question (important):

        Even though the value 128 is equal to 1000 0000 in binary, and 255 is equal to 1111 1111 in binary, so what's difference between std::bitset<128> and std::bitset<255> ?

        • Alex

          > So the inputed number in std::bitset as the size is not bits' number ; it is their values and must be equal to our flags.

          I read this a bunch of times and I'm not sure what you're trying to say.

          This line defines a std::bitset with a size of 8 bits, and initializes those bits to 0b'0000'0010. This is fine.

          This is invalid, as o2 is decimal value 8, and 8 is outside the range of our bitset. You actually meant:

          I use a char here because I want 8 bits, and unsigned because we should always use unsigned variables when dealing with bits. Bool is typically used for logical operations, not bitwise operations. It's bad practice to use bool in a bitwise context. I'm also not sure how well defined it is for use with bitwise operations.

          std::bitset<128> should define a bit field that holds 128 bits, and std::bitset<256> should define a bit field that holds 256 bits.

  • a700

    Hi, can you explain how this goes?
    if (myflags & option4)
        std::cout << "myflags has option 4 set";

    • bitwise-ands myflags with ...10000, ie. the result is all 0, and the fifth bit from the right is the same as in @myflags.
      If @myflags doesn't have this bit set, the result is 0.
      Non-zero integers evaluate to true, 0 evaluates to false.
      If the fifth bit from the right is set in @myflags, the condition is true.

  • Senna

    Hi,
    Why this webpage is broken down these days ?
    Is it temporary ?
    Don't stop supporting it, please.
    There's no source as simple, full contents as like learncpp.

    • Hi Senna!

      Quoting the index: "Feb 15: [Site News] Our server died yesterday and had to be restored from backups. We’re in the process of getting everything restored and reconfigured. If you find anything broken, please let us know here. Sorry for the inconvenience."

      If you want to continue reading while learncpp is down, you can do so on archive.org
      http://web.archive.org/web/20190214123506/https://www.learncpp.com/

    • Alex

      Yup, there was a hardware failure on the server. The site has been moved to a new server and should be up and running full-time (at least, until the next catastrophe). :)

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