67,108,864

We're working on a new series that will help us get a better understanding of SACD's vs. good old CD's. At the heart of everything is really two competing digital audio schemes: DSD (PDM) vs. PCM. In yesterday's post we learned that these two competing formats both use single bits known as 1's and 0's, which are square waves, to represent the original analog information we started with. But how? How is it possible to represent a complex changing analog voltage with only 1's and 0's? Our first clue to this mystery was presented yesterday when I demonstrated how an old fashioned telegraph system using 1-bit Morse Code can encode, transmit and decode language. This is actually pretty amazing if you think about it. Using only 2 states and the gaps between the two states one could endeavor to accurately transmit anything from entire musical scores, complex volumes of scientific knowledge, to just "howdy, I am arriving on the 6:30 train". But let's step back just a little to help our understanding. Morse Code was designed to represent language, itself a much earlier code base used to represent millions of combinations of letters we call words. The entire English language is based on 26 letters (symbols) and modern numbers are based on but 10 symbols. So Morse had to come up with a scheme to represent a total of 36 symbols (26 letters and 10 numbers) using only an on/off telegraph key. He did this not with a binary (two) system but, in fact, with a quinary system (5) that took advantage of short and long pulses coupled with short, medium and in between gaps. This formed a code upon a code: one would have to first understand written language then convert that language into a secondary code and back again. Why is this important to understand? Because it is the key to how a small code can represent a huge and complex pool of information or data. Language works because it is a code that uses only 26 symbols to represent millions of words - a seemingly infinite number of words in fact. Is there a limit to the number of words using only 26 symbols? Sure there is and that number happens to be67,108,864. We know that because in effect, the English language is the equivalent of a 26 bit system (sound familiar?). We calculate the number of possible combinations of on or off (in language it means letter there or not there) by the simple equation 2^Xand in the case of language it would be 2²⁶or67,108,864 possible combinations. If we then represent each letter with another code, like Morse Code, we can get an even smaller code base because we only need 5 bits to represent all 26 letters and most of the numbers. So this is how code upon code can take67,108,864 possible words and send them over a wire using only on, off and wait. Amazing, eh? Well if you can wrap your head around the notion that language is really just another code that represents millions of combinations, then our journey tomorrow will be a lot easier. Why? Because we understand that music and speech are also codes of sorts, converted from one form to another. So tomorrow we'll use what we've learned to understand the first of the two formats, PCM.