# Double Your Bits, Double Your Fun

If you own a digital desk, either in hardware or software, then youroutinely throw away from two to eight bits of your hard-earned 24. AsI asked last month, should you care? Not really, because you can't doanything about it. But you can work smarter within the constraintsimposed by necessity. This time around, we're gonna take a look at oneof the most basic questions a budding audio novice asks: “Mommy,why do we need 24 bits when our hearing's only 20?”

Let's start with young Elizabeth's question. Her mom has told hertime and again that her hearing has a range of about 120 decibels fromthe quietest perceptible sound to the “threshold of pain,”the loudest sound pressure tolerable before instantaneous hearingdamage occurs. Even though — when considering our hearing'sdynamic range — we are talking about sound-pressure level, we canstill use the same ratio measuring system — the decibel or dB— to measure the dynamic range represented by AES data. Twentybits' worth of dynamic range is about 120 dB, as each PCM bitrepresents about 6 dB of amplitude. So, young Liz has nailed thenumber, and to answer her question, we need to look at gain staging:juggling gain through a complex system to maximize resulting dynamicrange and minimize accumulated noise.

Okay, think about this: Take two signals — acoustic, analog ordigital — and add them together. The resulting mix is usuallylouder, though there are exceptions. Take that concept and apply it notonly to mixing, but EQ'ing and processing, and you can see that,without a bit of forethought on the part of a system designer orengineer, the final gain will either not take advantage of the dynamicrange available in the system or will quickly overload some bus. Toolittle or too much, neither is good, and usually the problem leanstoward too much signal and not enough dynamic range in which to fitit.

So, how does a designer deal with this dilemma? Well, rememberearlier when I said that a PCM bit encodes about 6 dB of dynamic range?Looking at that from another angle, you can think of dynamic range asbeing expressed as word length: A word length of 16 bits encodesroughly 16 times 6 dB, or 96 dB of dynamic range; and a 20-bit wordencodes about 120 dB. The AES/EBU protocol can carry a 24-bit essence,enough for a solid 20 bits of signal (thank you, young Elizabeth), plusfour additional low-level bits generated by processing.

Now that we're past the basics, let's look at one of the mostoverlooked features of better-quality digital audio geegaws and thewhole point of this month's column. A bonus for the discriminatingbuyer and a boon to those who value retention of low-amplitude detail,double-precision calculations are one of the keys to better bits.Double-precision is akin to the American Way: If some is good, more isbetter. Most products use single- precision arithmetic, though, if youdig a bit (yuk yuk), you find a few pearls in among the swine.Double-precision fixed-point would employ two times 24, or a 48-bitword length; double-precision floating-point would use a two times 32,or 64-bit mantissa. Twice as many bits allows low-amplitude details tobe retained rather than lost to rounding or truncation. Low-amplitudesignal retention is one area where a DSP programmer distinguishes himor herself, as I feel this is a key differentiation between trulyprofessional products.

<p> <p>NUMBER OF CHANNELS TO MIX</p> </p> | <p> <p>GAIN REDUCTION IN DB PER CHANNEL</p> </p> | <p> <p>3</p> </p> |
---|---|---|

4 | 2 | — |

8 | 3 | 4 |

16 | 4 | 8 |

24 | 5 | 8 |

32 | 5 | 8 |

48 | 6 | 16 |

64 | 6 | 16 |

80 | 7 | 16 |

112 | 7 | 32 |

144 | 8 | 32 |

176 | 8 | 32 |

240 | 8 | 64 |

304 | 9 | 64 |

So, how do twice as many bits help retain subtle details in yourmaterial? Here's an example: Take two numbers, representing theinstantaneous amplitude of signal and some amount of gain change beingapplied to that signal:

0.92 [original signal amplitude] × 0.707 [negative gain] =0.65044 [resultant signal amplitude after gain change].

Notice that the result of multiplying those numbers produces a newnumber with many more digits than what we started with. Think of howmany gain changes — which includes panning, EQ and mixing —occur during the course of a typical project, and you'll get some ideaof how 24-fixed or 32-floating bits can get “filled up”rather quickly. Those low-order bits, say the 22nd through 24th, carrylow-amplitude detail in the data.

Another example — basic gain staging in a digital mixer— should drive the point home. When two or more signals aresummed or mixed, the result is usually louder than either source. Thetable below shows a chart of the amount of “padding,” as itwas called in the analog days, or negative gain needed vs. the numberof channels being mixed in order to prevent overload in the downstreammix bus.

Looking at those numbers, it's plain to see that with 144 channelsto mix, a whopping 8 bits of gain reduction must be applied to eachinput channel prior to mixing. Those eight lower-order bits, thequietest stuff, must be handled in one of four ways: truncated ortossed away, the cheese-ball approach; rounded up or down to thenearest integer, a better method; re-dithered and wordlength-reduced,better still; or stored as double-precision.

Storing the data as double-precision retains most of thelow-amplitude detail and postpones the inevitable wordlength reductionuntil the end of the production cycle. However, understand that thereisn't a standard for double-precision data interchange betweenproducts, so files and AES/EBU output both end up as single-precisionbetween processing islands in the production chain. Still, a fewhost-based DAWs, such as Audio- Cube and Sonar XL, havedouble-precision modes, while SonicStudio HD, a hardware-based DAW, isfully double-precision throughout. The Cakewalk folks at Twelve ToneSystems advertise Sonar XL as having “all of the capabilities ofSonar, plus two 64-bit, fully automatable DirectX 8 masteringeffects.” Notice the mention of “64-bit,” whichindicates that the plug-ins are double-precision floating-point. Myguess is that more gear will join this elite list as vendors attempt todifferentiate their offerings based on quality rather than price.

I hope that this month's rant hasn't caused your head to rotate attoo high a speed and has helped you to understand why some gear soundslike crap at any setting except 11. Hopefully, it will also aid you inmaking more informed decisions when you need to choose or expand yourtechnology base in days to come.

*This column was written while under the influence of the originalquadraphonic version of Mike Oldfield's* Tubular Bells. *For adownloadable spreadsheet of the table, along with lots of hand-tooledlinks and useful information, head on over to*www.seneschal.net.

**Need help gain-staging in your digital mixer? Download this handy chart. (Excel format)**