The octal numeral system is a base 8 numeral system. It uses the numerals 0 through 7. The system is similar to binary (base 2) and hexadecimal (base 16). Octal numerals are written using the letter o before the numeral, for example, o04 or o1242. Octal numbers are also sometimes written with a small 8 to the lower right, as in 1242_{8}.
At one time, the octal system was used mainly for work with computers. It provided an easier way to work with binary numbers. As computers changed from using 24bit systems to 32 and 64bit systems, hexadecimal replaced octal for most uses. Certain groups, for example, Native Americans using the Yuki language in California and the Pamean languages^{[1]} in Mexico, also use an octal numbering system. They do this because when they count, they use the spaces between their fingers instead of counting the actual fingers.
Octal and binary
The octal numeral system uses a "threebit" binary coding. Each digit in an octal numeral is the same as three digits in a binary numeral. The grouping of the binary digits is done from right to left. The first three binary digits from the right are grouped into the last part of the octal numeral, then the next three digits form the next to the last part of the numeral.
Octal 
Binary

1 
001

2 
010

3 
011

4 
100

5 
101

6 
110

7 
111

10 
001 000


Octal 
Binary

11 
001 001

12 
001 010

36 
011 110

45 
100 101

53 
101 011

64 
110 100

100 
001 000 000

357 
011 101 111


Binary 
Groupings 
Octal

11 



011 
3

010111 


010 
111 
27

101000110 

101 
000 
110 
506

01011010101 
001 
011 
010 
101 
1325


Octal and decimal
In the decimal system (base 10), each digit in octal is equal to that digit multiplied by the exponent of 8 that is equal to its location minus one.

Location

6 
5 
4 
3 
2 
1

Value

32768 (8^{5}) 
4096 (8^{4}) 
512 (8^{3}) 
64 (8^{2}) 
8(8^{1}) 
1 (8^{0})

Example: o3425 to decimal

Octal 

Decimal

o3425 
= 
( 5 × 1 ) 
+ 
( 2 × 8) 
+ 
( 4 × 64 ) 
+ 
( 3 × 512)

= 
5 
+ 
16 
+ 
256 
+ 
1536

o3425 
= 
1813


Octal and hexadecimal
Octal is similar to hexadecimal because they are both easily converted to binary. Where octal is equal to threedigit binary, hexadecimal is equal to fourdigit binary. Where octal numerals start with the letter "o", hexadecimal numerals end with the letter "h". The easiest way to convert from one to the other is to convert to binary and then to the other system.
Octal 
Binary 
Hexadecimal

three digit 
four digit

o4 




100 



0100 
04h

o15 



001 
101 



1101 
0Dh

o306 


011 
000 
110 


1100 
0110 
C6h

o54253 
101 
100 
010 
101 
011 
0101 
1000 
1010 
1011 
58ABh

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References
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