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#### 6.1.1.2 Octal and Hexadecimal Numbers

In `awk`, all numbers are in decimal (i.e., base 10). Many other programming languages allow you to specify numbers in other bases, often octal (base 8) and hexadecimal (base 16). In octal, the numbers go 0, 1, 2, 3, 4, 5, 6, 7, 10, 11, 12, and so on. Just as ‘11’ in decimal is 1 times 10 plus 1, so ‘11’ in octal is 1 times 8 plus 1. This equals 9 in decimal. In hexadecimal, there are 16 digits. Because the everyday decimal number system only has ten digits (‘0’–‘9’), the letters ‘a’ through ‘f’ represent the rest. (Case in the letters is usually irrelevant; hexadecimal ‘a’ and ‘A’ have the same value.) Thus, ‘11’ in hexadecimal is 1 times 16 plus 1, which equals 17 in decimal.

Just by looking at plain ‘11’, you can’t tell what base it’s in. So, in C, C++, and other languages derived from C, there is a special notation to signify the base. Octal numbers start with a leading ‘0’, and hexadecimal numbers start with a leading ‘0x’ or ‘0X’:

`11`

Decimal value 11

`011`

Octal 11, decimal value 9

`0x11`

Hexadecimal 11, decimal value 17

This example shows the difference:

```\$ gawk 'BEGIN { printf "%d, %d, %d\n", 011, 11, 0x11 }'
-| 9, 11, 17
```

Being able to use octal and hexadecimal constants in your programs is most useful when working with data that cannot be represented conveniently as characters or as regular numbers, such as binary data of various sorts.

`gawk` allows the use of octal and hexadecimal constants in your program text. However, such numbers in the input data are not treated differently; doing so by default would break old programs. (If you really need to do this, use the --non-decimal-data command-line option; see section Allowing Nondecimal Input Data.) If you have octal or hexadecimal data, you can use the `strtonum()` function (see section String-Manipulation Functions) to convert the data into a number. Most of the time, you will want to use octal or hexadecimal constants when working with the built-in bit-manipulation functions; see Bit-Manipulation Functions for more information.

Unlike in some early C implementations, ‘8’ and ‘9’ are not valid in octal constants. For example, `gawk` treats ‘018’ as decimal 18:

```\$ gawk 'BEGIN { print "021 is", 021 ; print 018 }'
-| 021 is 17
-| 18
```

Octal and hexadecimal source code constants are a `gawk` extension. If `gawk` is in compatibility mode (see section Command-Line Options), they are not available.

 A Constant’s Base Does Not Affect Its Value Once a numeric constant has been converted internally into a number, `gawk` no longer remembers what the original form of the constant was; the internal value is always used. This has particular consequences for conversion of numbers to strings: ```\$ gawk 'BEGIN { printf "0x11 is <%s>\n", 0x11 }' -| 0x11 is <17> ```

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