Bitwise in storing boolean values

Bitmask is a technique that uses bitwise operations to store many true/false flags in a single integer with many advantages:

Memory efficient: it only costs 1 bit per flag -> 32 flags for an integer
Faster: Bitwise operations are faster than array operations

Let’s take some examples

1. Unix file permissions

On Unix-like systems, if we run ls -l on a file.

➜  ~ ls -l users.csv
-rw-r--r--@ 1 danieldang  staff  5218 Sep 19  2024 users.csv

Notice the -rw-r--r-- Except for the first character which is the file type. The rest 9 characters are the file permissions.

That 9 characters are 3 sets of rwx of each user: owner, group, other. (Also 9 bits in binary)

Character	Octal	Binary
`r`	4	100
`w`	2	010
`x`	1	001

rwx: 4+2+1 = 7 (octal) -> 100 | 010 | 001 = 111 (binary)
rw-: 4+2 = 6 (octal) -> 100 | 010 = 110 (binary)
r--: 4 (octal) -> 100 (binary)

If we use chmod 755 to set the file permissions, it will be:

7 = 111 = rwx   (owner)
5 = 101 = r-x   (group)
5 = 101 = r-x   (others)

When the computer checks the write permissions of the owner, it will be something like:

111 & 010 = 010 -> true

2. MAVLink protocol

MAVLink is a protocol for communicating with drones. Many of the messages are using bitmask to store the drone status.

Take SYS_STATUS message as an example:

There are 3 fields in 32-bit integer:

Field	Type	Description
onboard_control_sensors_present	uint32_t	Bitmap showing which onboard controllers and sensors are present. Value of 0: not present. Value of 1: present.
onboard_control_sensors_enabled	uint32_t	Bitmap showing which onboard controllers and sensors are enabled: Value of 0: not enabled. Value of 1: enabled.
onboard_control_sensors_health	uint32_t	Bitmap showing which onboard controllers and sensors have an error (or are operational). Value of 0: error. Value of 1: healthy.

And the defined sensor map are (there are more):

ID	Sensor	Hex	Description
1	MAV_SYS_STATUS_SENSOR_3D_GYRO	0x00000001	3D gyro
2	MAV_SYS_STATUS_SENSOR_3D_ACCEL	0x00000002	3D accelerometer
…	…	…	…
32	MAV_SYS_STATUS_SENSOR_GPS	0x00000020	GPS
33554432	MAV_SYS_STATUS_SENSOR_BATTERY	0x2000000	Battery
268435456	MAV_SYS_STATUS_PREARM_CHECK	0x10000000	pre-arm check status. Always healthy when armed
…	…	…	…

Let’s take a real example:

{
  "onboard_control_sensors_present": 325188671,
  "onboard_control_sensors_enabled": 274857023,
  "onboard_control_sensors_health": 57801791
}

present: 0001 0011 0110 0001 1111 1100 0011 1111
enabled: 0001 0000 0110 0001 1111 1100 0011 1111
health: 0000 1110 0001 0001 1111 1100 0011 1111

GPS:
present & 0x00000020 = 0x00000020 -> true
enabled & 0x00000020 = 0x00000020 -> true
health & 0x00000020 = 0x00000020 -> true
-> GPS is present, enabled, and healthy

Battery:
present & 0x2000000 = 0x2000000 -> true
enabled & 0x2000000 = 0x00000000 -> false
health & 0x2000000 = 0x2000000 -> true
-> Battery is present, NOT enabled, and healthy

Pre-arm check:
present & 0x10000000 = 0x10000000 -> true
enabled & 0x10000000 = 0x10000000 -> true
health & 0x10000000 = 0x00000000 -> false
-> Pre-arm check is present, enabled, and NOT healthy