Shows the steps involved in converting a number from a given base to base 10
# 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 "Convert the base $base number $number to a
base 10 number:";
print "Convert the integer component ($integer) of the
number:";
// 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 ($pos):
";
print "$digit * $base$pos = $result
";
$sums[] = $result;
}
print '
';
if (isset ($decimal))
{
print "Convert the decimal component (0.$decimal)
of the number:";
// 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
($pos):
";
print "$digit * 1/$base$pos =
$result
";
$sums[] = $result;
}
print '
';
}
$sums = implode (' + ', $sums);
eval ("\$base_10_value = $sums;");
print "
The value of the base $base number
$number in base 10 is $base_10_value.
";
print "This number is derived from the sum of the values
of the previous operations ($sums).
";
}
/*
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. :)