Properties of Digital Information
May 28, 2012 2 Comments
The digital computer can recognize only 1 and 0. Because it distinguishes only two signals, the intermediate signal cannot exist. This is the remarkable feature of digital information. According to Wikipedia, historical digital systems are the written text, Morse code and etc. They are the serial sequence of restricted characters. They can be converted into each other. The alphabet can be converted into 1 and 0.
The above figure is the example of the conversion. The upper row represents alphabets, and the lower row represents corresponding binary digits according to the ASCII code. Why is the conversion possible? Each character of any kind of digital information has common features, which are properties of the natural number one. As I say in “What Is the Natural Number One?“, it is indivisible, invariable and equal to each other. These properties are the basic property of digital data. However, there are some differences between digital data and natural numbers.
Digital data consists of multiple characters. In contrast, the natural number is the set of the natural number one only. Furthermore, we can add two natural numbers. However, we cannot apply the calculation rule to the ASCII code. Rather, 0 and 1 of the ASCII code are regarded as mere symbols. Especially, the digital data 0 and the number 0 are very different. Though digital data 0 is indivisible, the number 0 is divisible.
0=0+0+0+•••+0
Thus, the digital data and the number is different. Still, they can be converted reciprocally. Especially, as mentioned in “the concrete basis of the number theory“, the ordinal number has the basic property of digital data, which is the basis of the conversion of digital data. Therefore, the basic property of digital data is necessary for the interconversion of the digital data and the interconversion between the digital data and the number.
About Kazuhiko Kotani
The Revolution of Mathematics 
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