What is the Notation Converter?

The Notation Converter is one of the Excel files that you can download from the Home Page of this website. You can use it to convert between the various numerical notations that are discussed by Sir Roger Penrose in his book "The Emperor's New Mind." These notations are called Unary, Binary, Expanded Binary, Denary, and Machine State Notation. This last one, the Machine State Notation, is not so much a numerical notation as it is the Transition Function for a Turing Machine, but it can be converted to any one of the other notations, and for that reason it can also be thought of as a numerical notation.

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The first Excel file that you can download from the Home Page of this website allows you to build and run your own Turing Machine. I'll explain shortly how this Notation Converter can be very useful when working with the Turing Machines you build.

However, even if you never build your own Turing Machine, you may still find this Notation Converter useful if you ever want to convert a Binary Number (base 2) to its equivalent Denary Number (base 10) or vice versa.

You can certainly use Google to search the internet and find other converters that allow you to convert between base 2 numbers and base 10 numbers. Some of them are a lot easier and quicker to use than the Notation Converter Excel file. However, this Notation Converter allows you to convert between numerical notations that are thousands of digits long.

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If you do build and run your own Turing Machine, you may find the Notation Converter useful if you'd like to easily know the value of the data that you are using with your Turing Machine.

For example, one of the sample Turing Machines that comes with the Excel file that allows you to build and run your own Turing Machine is the one that Roger Penrose called XNx2. It reads in a number in Expanded Binary notation, doubles it, and writes out the answer in Expanded Binary notation.

Suppose you wanted to try out the XNx2 Turing Machine using the number 87. Then, what you can do is first use the Notation Converter to convert the number 87 from Denary notation to Expanded Binary notation. Then, you can build the XNx2 Turing Machine, and when you run it, you provide it with the Expanded Binary number that you got from the Notation Converter. When the Turing Machine stops running, you can take the answer it gave you and use the Notation Converter to convert it from Expanded Binary notation to Denary notation. If all goes well, you should see that the answer is 174.

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The Notation Converter is especially useful if you want to build your own Turing Machine and then try it out with the Universal Turing Machine.

To build the Universal Turing Machine, you will need to provide it with the Turing Machine Number of the Turing Machine that you want to emulate. So, the best way to proceed is to first use the Notation Converter to convert the instructions (in Machine State Notation) of your Turing Machine into a Binary number. This Binary number is really the Turing Machine Number of your Turing Machine.

Then, as your are building the Universal Turing Machine, you get the Turing Machine Number from the Notation Converter Excel file, from the sheet where the Turing Machine Number was calculated.

Any Turing Machine that does anything useful and worthwhile will usually have thousands of instructions. The Turing Machine Number of such a Turing Machine will likewise have thousands of digits. Although it is possible to compute the Turing Machine Number by hand, the best way to do it in a timely manner and without errors is by using the Notation Converter.

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It probably would be worth your time to watch some demo videos that show what I was just trying to verbally explain. I shall now tell you how you can find these demo videos in this website.

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First, notice that at the top of this web page, there is a link called FAQ's. Go ahead and click on it.

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Then, when you're on that page, click on the following question:

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Then, when you're on that page, click on any one of the following, all of which are video demos having to do with the Notation Converter.

If you are interested in downloading and using the Notation Converter, then I think you'll find the above three videos to be very helpful.