A bitmask is a mask (think of a multiple choice grading key) used to manipulate or reveal values in a bitmask. But to understand what a bitmask is we first need to understand what a bitfield is.
What is a Bitfield
A bitfield is a collection of values that each represent one of two states, or, using a more familiar metaphor - a row of household switches on a wall, each representing whether the lights are on or off in different rooms or areas around the house. We will use the following image as a tangible example.
Bits and Bytes
A bit is the smallest piece or data that is used in digital systems such as that in computers. A single bit can either be "on" or "off", or 1 or 0.
A collection of 4 bits is called a nibble, 8 bits a byte, 16 bits a halfword and 32 bits a word.
Bitfield
Thus, a bitfield is a collection of two or more bits and can be represented by one of the data sizes above but don't have to.
The Household Example
In the example image we have the lights in the house in the following states:
Living Room | Kitchen | Bedroom | Garage |
---|---|---|---|
off |
on |
off |
on |
If off
is the same as 0
and on
is the same as 1
, then:
Living Room | Kitchen | Bedroom | Garage |
---|---|---|---|
0 |
1 |
0 |
1 |
And that, is a bitfield - 0101
in this case.
Decimal and Binary
This collection of ones and zeros is what known as the known as binary numeral system. The binary numeral system is known as a base 2 numeral system. This means that one can only use the two symbols 1 and 0 to express mathematical and computational information.
We humans use the decimal numeral system which is classified as a base 10 numeral system and consists of the ten symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
We won't go into how to convert from decimal to binary and back, but the following table should support the explanation and example.
Binary | Decimal |
---|---|
0000 | 0 |
0001 | 1 |
0010 | 2 |
0011 | 3 |
0100 | 4 |
0101 | 5 |
0110 | 6 |
0111 | 7 |
1000 | 8 |
1001 | 9 |
1010 | 10 |
1011 | 11 |
1100 | 12 |
1101 | 13 |
1110 | 14 |
1111 | 15 |
Does this look familiar? According to this table, the current state of the lighting situation in the house can be represented as 5
🤯. So, instead of using four different variables/containers, each with their own size, to store the collective light-switch-state of the house, we can represent the same data with only one.
Expressed in JavaScript:
// Instead of...
const houseLights = {
livingRoom: false, // Boolean with a size of 8 bytes
kitchen: true, // Boolean with a size of 8 bytes
bedroom: false, // Boolean with a size of 8 bytes
garage: true, // Boolean with a size of 8 bytes
};
// We can do this...
let houseLights = 5; // Number with a size of 8 bytes
// 5 can be represented as 0b0101
The Benefits of Bitfields
Space-Saving
And this is where the first benefit of using bitfields comes in - they are a more compact i.e. space-saving, way of storing data.
In the JavaScript code above, if we assume that an empty object in JavaScript consumes zero bytes in memory (which doesn't of course in reality), then the object of four "light switches", each represented as a boolean (which take up 8 bytes¹ each), will consume a conservative 32 bytes on a 64-bit system.
If we used a number to represent the same data we would only be using 8 bytes of memory on the same 64-bit system.
Similarly, these savings appear clearer (as an empty struct consumes zero bytes) in C:
struct {
bool living_room_light; // int with a size of 8 bytes
bool kitchen_light; // int with a size of 8 bytes
bool bedroom_light; // int with a size of 8 bytes
bool garage_light; // int with a size of 8 bytes
} house_lights = {
.living_room_light = false,
.kitchen_light = true,
.bedroom_light = false,
.garage_light = true,
};
// Versus...
int house_lights = 5; // int with a size of 8 bytes
// 5 can be represented as 0b0101
C does not have a boolean data type. The bool
syntax above is syntactic sugar for int
- an integer. Here the struct of bool
i.e. int
s, consumes 32 bytes in a 64-bit system while the int
only consumes 8 bytes on the same system.
Easier To Query and Manipulate
And, finally we get to the part about bitmasks.
In order to query/read or manipulate values in the bitfield, we use bitwise operations. Bitwise operators are operators that operate on single bits. These operators are: AND, OR, NOT, XOR (exclusive-or).
Given that bits are either 1 or 0 we can further explain OR, AND and NOT below.
OR
One or both input values should to be 1
for the output to be 1
. The symbol |
is used in C-style programming languages to represent this bitwise operator.
1 OR 1 = 1
1 OR 0 = 1
0 OR 1 = 1
0 OR 0 = 0
AND
Both input values should to be 1
for the output to be 1
. The symbol &
is used in C-style programming languages to represent this bitwise operator.
1 AND 1 = 1
1 AND 0 = 0
0 AND 1 = 0
0 AND 0 = 0
NOT
NOT takes only one input and inverts the output. The symbol ~
is used in C-style programming languages to represent this bitwise operator.
Some more benefits of bitfields can be found in the footnotes².
OK, if you're still awake 😅, let's continue.
Checking Which Lights Are On
Using our house-hold example, we have a bitfield of:
Living Room | Kitchen | Bedroom | Garage |
---|---|---|---|
0 |
1 |
0 |
1 |
If we have a variable called house_lights
and want to know whether the kitchen lights are on, we would use the AND bitwise operator.
living room kitchen bedroom garage
house_lights = 0 1 0 1
kitchen_light = 0 1 0 0
// ANDing these two bitfields together we get:
0101 // 5
AND 0100 // 4
----
0100 // 4
So we can say: if we AND the house_lights
and the kitchen_light
together and the result is equal to kitchen_light
, then the kitchen light is on.
We can use the binary to decimal table from before to get the decimal values we need or use the prefix 0b
(in most C-style languages) to display the binary directly. We can then write the above pseudocode in C as:
int house_lights = 0b0101; // 5
int kitchen_light = 0b0100; // 4
bool is_kitchen_light_on = house_lights & kitchen_light;
// is_kitchen_light_on = true
Switching Lights On
Similarly, if we want to turn a light/bit on we use the OR bitwise operator like so:
living room kitchen bedroom garage
house_lights = 0 1 0 1
bedroom_light = 0 0 1 0
// ORing these two bitfields together we get:
0101 // 5
OR 0010 // 2
----
0111 // 7
So we can say: if we OR the house_lights
and the bedroom_light
together, the result is the new value/state for house_lights
, with the kitchen, bedroom and garage lights on.
Representing the above pseudocode in C:
int house_lights = 0b0101; // 5
int bedroom_light = 0b0010; // 2
int new_house_lights = house_lights | bedroom_light;
// new_house_lights = 0b0111 or 7
The state of the house lights are now:
Living Room | Kitchen | Bedroom | Garage |
---|---|---|---|
0 |
1 |
1 |
1 |
off |
on |
on |
on |
Switching Lights Off
Using a combination of bitwise AND and NOT we can turn turn one of the switches off i.e. flip a bit from 1 to 0.
int house_lights = 0b0101; // 5
int garage_light = 0b0001; // 1
int new_house_lights = house_lights & ~(house_lights & garage_light);
// new_house_lights = 0b0100 or 4
Here, on the 4th line, we AND the house_lights
and the switch we want to turn off, garage_light
in this case, we NOT that result and, finally, AND that result with the original house_lights
. Further illustrated:
living room kitchen bedroom garage
house_lights = 0 1 0 1
garage_light = 0 0 0 1
// ANDing these two bitfields together we get:
0101 // 5
AND 0001 // 1
----
0001 // 1
// NOTing this value we get:
NOT 0001 // 1
----
1110 // 14
// And ANDing this result with the original house_lights we get:
0101 // 5
AND 1110 // 14
----
0100 // 4
And that summarises what bitmasks are and how to use them.
Footnotes
- A boolean in JavaScript actually has a size of 1 byte, but byte alignment on 32-bit systems will cause 4 bytes to be used and 8 bytes on 64-bit systems.
- Other Benefits of Bitfields
- Performance - reading or manipulating a single string of bits at a time is faster than doing so on separate variables
- Cache Efficiency - one can improve cache efficiency when using bitfields as usually one or more can fit in a cache line
- Readability and Maintainability - while bitfields seem hard to read and understand at first they allow one to organise a complex combination of flags into a single variable (name)
- Reduced Code Size - using bitfields can greatly reduce code as a single operation can be done on one line as opposed to setting multiple separate variables
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