Can I really "erase" data?

Computer data and files are made up of numbers. Strings of 1's and 0's. To derive meaning from the digits you must organize them into patterns. Once your computer arranges the numbers into patterns, voila- you have your files. When the strings of numbers at the beginning of the sequence are scrambled, or randomized, the whole thing- be it a picture, email or website, the whole file is rendered invisible. Once the "deleted" or invisible file is erased, the computer sees the space where the file has been as blank. Then, new files and applications can be placed upon its old spot. As more and more 1's and 0's pile up over the grave site of the old file, eventually the file is erased. Sometimes the erasure does not completely occur because the "overwriting" process occurs at random. If any portion of the deleted file is not written over, that file can be recovered. If you think about this, then, when you sell off your old system, much of your data that has been "erased" may still be accessed.