The umask value is a four-digit octal number that determines the default permissions for new files and directories created by a user. The umask value specifies the permissions that are not granted to the user, group, and others. The permissions are represented by three bits for each category, where 1 means execute, 2 means write, and 4 means read. The sum of these values indicates the combination of permissions. For example, 7 means read, write, and execute; 6 means read and write; 5 means read and execute; 4 means read only; 3 means write and execute; 2 means write only; 1 means execute only; and 0 means no permission.

The umask value is subtracted from the maximum permissions for files and directories, which are 666 and 777, respectively. The maximum permissions are then converted to binary and bitwise ANDed with the bitwise complement of the umask value. The result is the default permissions for the new files and directories. For example, if the umask value is 0027, the default permissions for a new file are:

666 - 027 = 639 639 in octal = 110 011 001 in binary 027 in octal = 000 010 111 in binary Bitwise complement of 027 = 111 101 000 in binary 110 011 001 AND 111 101 000 = 110 001 000 in binary 110 001 000 in binary = 608 in octal 608 in octal = rw- — —

The default permissions for a new directory are:

777 - 027 = 750 750 in octal = 111 101 000 in binary 027 in octal = 000 010 111 in binary Bitwise complement of 027 = 111 101 000 in binary 111 101 000 AND 111 101 000 = 111 101 000 in binary 111 101 000 in binary = 750 in octal 750 in octal = rwx r-x —

Therefore, the umask value of 0027 ensures that new files can be read and written by their owning user, and are not accessible at all for everyone else. New directories can be read, written and listed by their owning user, read and listed by their owning group, and are not accessible at all for everyone else.

References:

Umask command in Linux with examples - GeeksforGeeks

What Is umask in Linux, and How Do You Use It? - How-To Geek

What is UMASK and how to set UMASK in Linux/Unix? - Kernel Talks