So, we're talking Javascript here. Right?

I'd give and id to the textarea and use that in my event call:

print "<textarea name='txtOutput' id='txtOutput' value='txtOutput' sty
+le='width: 250px'></textarea>";
print "<input type='radio' name='cbox' value='alice'  selected onClick
+='char_value()'/>Char Value";
print "<input type='radio' name='cbox' value='' onClick= '32bits_value
+(document.getElementById(\'txtOutput\').value)'/>32bits value";
[download]

Untested.