Octal

Octal is another number system with less symbols to use than our conventional number system. Octal is fancy for Base Eight meaning eight symbols are used to represent all the quantities. They are 0, 1, 2, 3, 4, 5, 6, and 7. When we count up one from the 7, we need a new placement to represent what we call 8 since an 8 doesn’t exist in Octal. So, after 7 is 10.

Octal 0 1 2 3 4 5 6 7 10 11 12… 17 20… 30… 77 100
Decimal 0 1 2 3 4 5 6 7 8 9 10… 15 16… 24… 63 64

Just like how we used powers of ten in decimal and powers of two in binary, to determine the value of a number we will use powers of 8 since this is Base Eight. Consider the number 3623 in base eight.

83 82 81 80
3 6 2 3
1536+384+16+3
1939

Each additional placement to the left has more value than it did in binary. The third digit from the right in binary only represented 23-1, which is 4. In octal, that is 83-1 which is 64.