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| Code | |||||
<?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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