Algorithms
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<?php
# Show the steps involved in converting a number
# from any base (like octal or hex) to base 10
# See below for examples, instructions and copyright
function show_convert_to_base_10 ($number, $base)
{
// If the number contains a decimal component
if (strstr ($number, '.'))
{
// Get the integer and decimal components
list ($integer, $decimal) = explode ('.', $number);
}
else
{
// The number is an integer
$integer = $number;
}
print "<b>Convert the base $base number $number to a
base 10 number:</b><blockquote>";
print "Convert the integer component ($integer) of the
number:<blockquote>";
// Compute the value of the integer component
// Loop through the integer digit by digit
// Reverse the number for easier handling
$integer = strrev ($integer);
$length = strlen ($integer);
for ($pos = 0; $pos < $length; ++$pos)
{
/*
PHP lets you treat strings and numbers like arrays
Specify an offset and get the character at that
position
*/
$digit = $integer[$pos];
// Handle character values for digits
// (for bases greater than 10)
if (eregi ('[a-z]', $digit))
{
$digit_value =
(ord (strtolower ($digit))
- ord ('a')) + 10;
$digit = "$digit ($digit_value)";
}
else
{
$digit_value = $digit;
}
// Multiply the current digit by the radix
// raised to the power of the current position
$result = $digit_value * pow ($base, $pos);
print "Multiply the value of the digit at position
$pos by the value of the radix ($base) raised
to the power of the position ($pos):<br />";
print "$digit * $base<sup>$pos</sup> = $result
<br /><br />";
$sums[] = $result;
}
print '</blockquote>';
if (isset ($decimal))
{
print "Convert the decimal component (0.$decimal)
of the number:<blockquote>";
// Pad the number with a leading 0 so that we can
// start at position 1
$decimal = '0'.$decimal;
$length = strlen ($decimal);
for ($pos = 1; $pos < $length; ++$pos) {
$digit = $decimal[$pos];
// Handle character values for digits
// (for bases greater than 10)
if (eregi ('[a-z]', $digit))
{
$digit_value =
(ord (strtolower ($digit))
- ord ('a')) + 10;
$digit = "$digit ($digit_value)";
}
else
{
$digit_value = $digit;
}
// Multiply the current digit by the radix
// raised to the power of the current position
$result = $digit_value * pow (1/$base, $pos);
print "Multiply the value of the digit at
position $pos by the value of the 1/radix
($base) raised to the power of the position
($pos):<br />";
print "$digit * 1/$base<sup>$pos</sup> =
$result<br /><br />";
$sums[] = $result;
}
print '</blockquote>';
}
$sums = implode (' + ', $sums);
eval ("$base_10_value = $sums;");
print "</blockquote>The value of the base $base number
$number in base 10 is $base_10_value. <br />";
print "This number is derived from the sum of the values
of the previous operations ($sums). <br /> <br />";
}
/*
DESCRIPTION
============================================================
show_convert_to_base_10:
Shows the steps involved in converting a number from a given
base to base 10. I wrote the example for a book, but after I
was mostly finished it, it seemed too off topic. I hope
that someone finds it useful. :)
============================================================
CREDITS
============================================================
Author: J. A. Greant ( zak@nucleus.com )
Version 1: November 19, 2000
============================================================
NOTICES
============================================================
If you:
Modify this code and want to share your changes :)
Find a bug
Have other questions or comments
Please write:
Zak Greant (zak@nucleus.com)
============================================================
USAGE EXAMPLES
============================================================
# Convert a hexadecimal number (base 16)
show_convert_to_base_10 ('FF', 16);
# Convert a binary number (base 2)
show_convert_to_base_10 ('1101001', 2);
# Convert a base 36 number
show_convert_to_base_10 ('1ab.00z9', 36);
============================================================
COPYRIGHT
============================================================
Copyright (c) 2000 J. A. Greant ( zak@nucleus.com )
All rights reserved.
This function is free software; you can redistribute it
and/or modify it under the terms of the GNU Lesser General
Public License as published by the Free Software Foundation;
either version 2.1 of the License, or (at your option) any
later version.
This function is distributed in the hope that it will be
useful,but WITHOUT ANY WARRANTY; without even the implied
warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
PURPOSE. See the GNU Lesser General Public License for more
details.
You should have received a copy of the GNU Lesser General
Public License along with this function; if not, write to
the:
Free Software Foundation, Inc.
59 Temple Place, Suite 330
Boston, MA
02111-1307 USA
http://www.gnu.org/
============================================================
*/
?>
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Usage Example
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# Convert a hexadecimal number (base 16)
show_convert_to_base_10 ('FF', 16);
# Convert a binary number (base 2)
show_convert_to_base_10 ('1101001', 2);
# Convert a base 36 number
show_convert_to_base_10 ('1ab.00z9', 36);
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