Octal numbers (base 8)

Like our "normal" numbers are base 10 (or radix 10) because we have 10 different digits (from the 0 to the 9): 


0123456789

the octals numbers include only the representations for the values from 0 to 7: 


01234567

and, therefore, its mathematical base is 8. In C++ octal numbers are denoted by beginning always with a 0 digit. Let's see how we would write the first numbers in octal: 

octal  decimal
-----  -------
  0       0   (zero)
 01       1   (one)
 02       2   (two)
 03       3   (three)
 04       4   (four)
 05       5   (five)
 06       6   (six)
 07       7   (seven)
010       8   (eight)
011       9   (nine)
012      10   (ten)
013      11   (eleven)
014      12   (twelve)
015      13   (thirteen)
016      14   (fourteen)
017      15   (fifteen)
020      16   (sixteen)
021      17   (seventeen)

Thus, for example, the number 17 (seventeen, or XVII in Roman) it is expressed 021 as an octal number in C++. We can apply the same mechanism that we saw previously for decimal numbers to the octal numbers simply by considering that its base is 8. For example, taking the octal number 071263:



therefore the octal number 071263 is expressed as 29363 in decimal numbers.