Data Question.

Factual Questions
1

Can you compress data by expressing a byte, as the byte^-X?
In other words can expressing data as a negative power of “X” save space?
Also is each byte unique? In other words, are there any combinations of the eight 1s or 0s in a byte that give the same value?

2

It’s hard to see how these could be serious questions, but since this is GQ, I’ll give you the benefit of the doubt. The answers are:

(1) No. It is possible to compress collections of bytes, but not (AFAIK) a single byte.

(2) By definition, each combination of binary digits represents a single number. In much the same way, each combination of decimal digits represents a single number.

3

Thanks for the response.

Anyway, how are these questions less important than anything else?

4

Sure you can. Consider this scheme to compress a byte:


if (original_data==00000000)
    emit 00;               /* two bits */
else if (original_data==11111111)
    emit 01;               /* two bits */
else
    emit 1, original_data; /* nine bits */

That is, two special bytes will be compressed to two bits each, and all other values will be “compressed” to nine bits. It’s a good compression scheme, if you expect a lot of bytes of all zeroes or all ones.

5

I will assume you mean a standard 8 bit byte. Given 8 bits, you can represent 2^8 different values. Examples are: 0 to 255, -128 to 127, your favorite 256 character set alphabet, a value of a color from full off to full on, and thousands, if not millions, of other uses of bytes. To use your example, and setting X to 1, note that encoding 4 as 1/4 means that you are using fractions and not integers. You have to devise a way to encode fractions in a byte. The more fractions you can encode the fewer integers you can encode: the total number of items you can represent will always be at most 256.

For the second question, what is your data that you are encoding in a byte? Some encodings might have some redundancy but most won’t. Of the most common uses of bytes, there’s a “semi-example” of negative 0. Regular zero is 00000000, but 10000000 is the same except the first bit (which represents sign) is negative. This value is treated in some systems nearly the same as 0 for mathematical purposes, but nowadays it is more commonly treated as -128. As for larger data types than bytes, in some floating point systems there can be multiple ways to represent the same number, especially if it is “Not A Number”.

MrNeutron gives a good example of the “no such thing as a free lunch” principle of data compression. If you make something smaller, other things must get bigger. See the comp.compression FAQ for more information