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# Hex to Octal Conversion - Octal to Hex Conversion

## Convert hexadecimal numbers into octal numbers and vice versa

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Hexadecimal numbers use a base-16 system. This means that they use 16 different digits, namely 0-9 and A-F. In this system, A stands for 10, B for 11, up to F which stands for 15. Hexadecimal numbers are particularly useful in computing because they provide a compact way to represent binary numbers. Each hexadecimal digit corresponds to exactly four binary digits, making them easy to convert.

Octal numbers, on the other hand, use a base-8 system. They therefore use 8 different digits: 0-7. Just like hexadecimal numbers, octal numbers have a direct relationship with binary numbers: each octal digit corresponds to three binary digits.

Both systems are therefore positional numeral systems, just like the decimal system that we use in everyday life. In a hexadecimal number, for example, the right position represents the units, the next position to the left the sixteens, then the two hundred and fifty-sixths, and so on. In an octal number, the right position represents the units, the next position to the left the eights, then the sixty-fourths, and so on.

Converting between hexadecimal and octal is not as straightforward as converting these systems to binary numbers, because 16 and 8 are not powers of each other. The conversion process usually goes through the binary system: hexadecimal is first converted to binary and then this binary number is converted to octal, or vice versa.

1 1
2 2
3 3
4 4
5 5
6 6
7 7
8 10
9 11
A 12
B 13
C 14
D 15
E 16
F 17