What is the name for storing / packing many boolean states into one number?

Question

It's a sort of simple compression where you use one numeric variable to store many boolean / binary states, using doubling and the fact that every doubling number is 1 + the sum of all the previous ones.

I'm sure it must be an old, well-known technique, I'd like to know what it's called to refer to it properly. I've done several searches on every way I can think of to describe it, but found nothing beyond some blog articles where the article authors seem to have figured this out themselves and don't know what to call it, either (example 1, example 2).

For example, here's a very simple implementation intended to illustrate the concept:

packStatesIntoNumber () {
  let num = 0
  if (this.stateA) num += 1
  if (this.stateB) num += 2
  if (this.stateC) num += 4
  if (this.stateD) num += 8
  if (this.stateE) num += 16
  if (this.stateF) num += 32
  return num
}

unpackStatesFromNumber (num) {
  assert(num < 64)
  this.stateF = num >= 32; if (this.stateF) num -= 32
  this.stateE = num >= 16; if (this.stateE) num -= 16
  this.stateD = num >= 8; if (this.stateD) num -= 8
  this.stateC = num >= 4; if (this.stateC) num -= 4
  this.stateB = num >= 2; if (this.stateB) num -= 2
  this.stateA = num >= 1; if (this.stateA) num -= 1
}

You could also use bitwise operators, base 2 number parsing, enums... There are many more efficient ways to implement it, I'm interested in the name of the approach more generally.

Answer 1

It's most commonly referred to as a bit field, and another term you'll often hear is bit masks, which are used to get or set individual bit values or the entire bit field at once.

Many programming languages have auxiliary structures to help with this. As @BernhardHiller notes in the comments, C# has enums with flags; Java has the EnumSet class.

Answer 2

Strange, quite a bit of different terms here but I don't see the one that came immediately to mind (and it's in the title of your question!)--Bit Packing is what I've always heard it termed.

I had thought this was really obvious but strangely when I google it this seems to be a term that is widely used but not officially defined (Wikipedia seems to redirect to bit field which is a way to do bit packing, but not a name for the process). Searching for the definition seems to lead to this page:

http://www.kinematicsoup.com/news/2016/9/6/data-compression-bit-packing-101

Which isn't great for SO purposes but it's the best definition/description I can find including this succinct description: "Bit-packing is a simple concept: Use as few bit as possible to store a piece of data."

Answer 3

There are many different terms used to describe this.

Most commonly the bits are called "bit flags" or "bit fields".
(However, it's worth noting that "bit fields" sometimes refers to a specific feature of the C and C++ languages, which is related but not exactly the same.)

The integer itself is referred to variously as either a "bit array", a "bit set" or a "bit vector", depending on usages and circumstances.

Either way, extracting the bits from the bit set/vector/array is done through shifting and masking.
(i.e. using a bit mask.)

---

For some examples of each term in active use:

• Wikipedia's article on the subject is titled Bit array, which notes that it is "also known as bit map, bit set, bit string, or bit vector"
• C++ uses std::bitset
• Java uses BitSet
• C# uses BitArray
• StackOverflow has the tags bitvector, bitarray and bitset
• On PyPi there is a bitarray project and a BitVector project

---

It's not really pertinent to the question but I'd like to say: please do not use addition and subtraction to set and clear bits as those methods are prone to error.
(i.e. if you do num += 1 twice, the result is equivalent to num += 2.)

Prefer to use the appropriate bitwise operations instead, if your chosen language provides them:

packStatesIntoNumber ()
{
  let num = 0
  if (this.stateA) num |= 1
  if (this.stateB) num |= 2
  if (this.stateC) num |= 4
  if (this.stateD) num |= 8
  if (this.stateE) num |= 16
  if (this.stateF) num |= 32
  return num
}

unpackStatesFromNumber (num)
{
  this.stateF = ((num & 32) != 0);
  this.stateE = ((num & 16) != 0);
  this.stateD = ((num & 8) != 0);
  this.stateC = ((num & 4) != 0);
  this.stateB = ((num & 2) != 0);
  this.stateA = ((num & 1) != 0);
}