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 be 67,108,864. 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 2X and in the case of language it would be 226 or 67,108,864 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 take 67,108,864 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.

Paul McGowan – PS Audio, Intl.

Telegraphing Music

I hope you’ll indulge me on this series as I want to take it in smaller, slower bites one day at a time. I do get mail from time to time from those that want longer more detailed posts and are antsy to not be required to wait each day for more info and to those I apologize.

My feeling on this particular subject is there’s a lot to learn and understand for many and it’s easier to grasp large complex issues in smaller more “edible” bites. It’s also easier for me to write them and give you content with substance.

Yesterday we covered a very basic view of digital audio vs. analog audio. Although there are numerous means of capturing, recording and playing back music other than analog, we’re going to be focusing on just two: Pulse Code Modulation (PCM) and Pulse Density Modulation (PDM or DSD or SACD).

Each of the two schemes we’re focused on use identical “bits” to work their magic. The bits are what you’re familiar with, 1′s and 0′s or, more descriptively, on and off states. These states are represented by simple square waves and, if you’ll remember back to our last series on power, a square wave is nothing more than a quick transition from 0 volts to + volts and then back again.

The easiest way to make a square wave is to use a battery and two wires. Connect the – wire of the battery to a DAC’s ground and take the + wire and connect it to the DAC’s digital input. To make a square wave, simply touch the + wire to the battery’s + terminal and then remove it. Each time you touch it and remove it, the DAC see’s what is known as a transition from 0 (no volts) to 1 (+ volts) and then back to 0. Do this multiple times in a row and you have a binary (meaning two states) “digital” data stream.

If you do this in a particular order of 1′s and 0′s you create a type of code and if a device is used to create this code it is known as an “encoder”. To unravel this code you need a “decoder” which can understand this code and give you a predetermined output based on this code. An ADC (Analog to Digital Converter) is a modern day analog to digital encoder and a DAC (Digital to Analog Converter) is a modern day digital to analog decoder that understands your “code” and puts everything back in original form.

But there are far more basic digital encoders and decoders we may be familiar with: namely people. Perhaps the best known of these human powered digital encoder/decoder schemes we would all be familiar with was invented by a fellow named Samuel Morse and later became known as Morse Code. The device he used was called the telegraph.

In 1836 Morse and a few other inventors were determined to send messages long distances with wires. Without getting too in depth on the history, Morse created a code of 1′s and 0′s that enabled an operator to convert language and numbers into a binary code and transmit that code over wires and be received many miles away and then reconverted back to its original form. As a point of interest, Morse couldn’t use on and off for his binary signal because the off state wouldn’t be recognized. Instead of on and off, Morse code used long and short – but the idea is exactly the same.

The beauty of this code scheme is that the quality of the conversion process, from language to binary and back again, could be all over the map and still work. That meant poor translators as well as expert translators could use the code to send intact precise messages down a wire and, eventually, through the air and the results would always be repeatable and identical.

Understanding how the telegraph is the same as digital music is important because the concept we’re going to understand is embodied in this scheme of encoding and decoding one form of data to another.
email Telegraphing music.

Paul McGowan – PS Audio, Intl.

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