Telling the truth

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In our ongoing series on the differences between CD's and SACD's we've covered the first part of the CD process, encoding audio into a digital format known as PCM, and next we're going to explain how we get the encoded data back into audio again so we can listen to it. The encoding process is handled by an ADC (Analog to Digital Converter) and the decoding process is handled by a DAC (Digital to Analog Converter). We've learned that the ADC took fixed point snapshots of the music signal and recorded them as a number that is directly relatable to the level of voltage contained in the musical signal. The sample rate of this process determines the number of snapshots we take in a second and the bit depth determines the size of the dynamic range we can record as well as how accurate our number that represents the voltage is. What we wind up with is a code that represents a voltage. If you were to take that coded bit stream and listen to what it sounds like through a pair of speakers you wouldn't be able to tell what the heck it was if you could even hear anything. In fact, if you didn't know what the digital signal was and how to decrypt its code, the entire stream would be meaningless to anyone looking. Why is this important to know? That you must decrypt the code before you can listen to it is one of the biggest differentiators between the CD format and the SACD format. But that's just a tease of what's coming later in this series. The basic principal of converting PCM back into analog is simpler to understand than how it got to be code in the first place. Remember that PCM is a code and we need a "magic decoder ring" to unlock its secrets? That code key is something known as a truth table. A truth table is the guide that the digital 1's and 0's use to count up to a number. Take a look at an example of a truth table. This is how a computer counts. Look at the left side 0 - 15 numbers. Pick any number on the left and then look at the little cells across from that number. Those cells are the on/off bits. Look at 1 and notice there is a 1 in the X1 column but all 0's in the other columns. Now look at 4 and notice how the first 4 have 1's the others have 0's. (For those of you familiar with an actual 8 bit binary counting scheme this isn't quite correct but that's not important for this discussion.) The point is we count by using either an on or an off in the appropriate column and the column should represent a factor of 2 (because this is all binary). OK, so each word comes in with the ability to turn on or off one of the columns and each column represents a factor of 2. Got it? Now it's a simple matter to make each column a voltage and each successive column with twice the voltage of the one before it. Now replace the 1's and 0's with switches. When a 1 appears in any column the switch is on and when there's a 0 the switch is off. Every time a switch is on, the amount of voltage in that column is added to the output. All switches on and you get a big voltage - all switches off no voltage - a few switches on a voltage somewhere in the middle. Here's a picture of that: So each bit can either turn on or not turn on one of the 16, 24, or 32 switches available to it in the DAC. When a switch is active, the voltage goes up. Now, remember that our goal is to have a digital number that represents a fixed voltage? That's how the process works and in the end we wind up with what I showed you yesterday, a sine wave (or musical signal) made from small steps of voltage generated by the 1's and 0's turning on or off the little voltage switches. That's how a classic ladder DAC works. But today, we no longer use this type of DAC. Tomorrow we'll review and explain what's up with that!
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Paul McGowan

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