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6.1.1.2 Octal and Hexadecimal Numbers
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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; *note Nondecimal Data::.)  If you have octal or hexadecimal
data, you can use the 'strtonum()' function (*note String 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 *note Bitwise 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 (*note 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>