ANSWERS: 2
  • The following answer was found at this site : http://www.prorec.com/prorec/articles.nsf/articles/EA68A9018C905AFB8625675400514576 ---------------------------------------- We now come to a relatively new, yet all-important dB designation, the “dBFS,” which stands for “decibels full scale” -- a kind of dB designation created especially for digital gear. This one is a little strange because, unlike all the other dB varieties, the reference level isn’t at the bottom, or somewhere near the middle, but at the very top possible measurement. This means that “0 dBFS” designates the highest possible level, and that all other measurements expressed in terms of dBFS will always be less than 0 dB -- in other words, a negative number. This is why, on digital gear using VU meters (where 0 dBVU means 0 dBFS), the “0” is at the top of the scale, and the meter can never read higher than that. Let’s take16 bit digital audio as an example. “The term “16-bit” means that the level of any sample can be stored as a 16-bit binary number (a binary number with 16 placeholders). As we know, the binary number system only has two digits, “0” and “1.” Therefore, the highest possible 16 bit binary number is the number with all “1”s: 1111 1111 1111 1111 (binary). So the formula for dBFS in a 16 bit digital system is: dBFS = 20 * log (sample level / 1111 1111 1111 1111) It’s easy to see why they say “you can’t go over 0 dB in digital.” That’s because, at the highest possible sample level (which is the dB reference level, in the case of digital): 20 * log (1111 1111 1111 1111 / 1111 1111 1111 1111) = 0 dBFS Also, using the same formula, we can easily figure out the dynamic range of a 16-bit system, because we know the smallest possible sample level (other than zero, of course) is 0000 0000 0000 0001. 20* log (0000 0000 0000 0001 / 1111 1111 1111 1111) = -96 dB So, now you know why the meters on a 16-bit DAW usually read from 0 dB to -96 dB, when displayed at their highest resolution. By following the same logic, it’s easy to figure out that the dynamic range of a 20-bit digital audio system is 120 dB, and that for 24-bit digital audio, it’s 144 dB. I’ll let you do the math if you want to. (Hint: on most calculators, it’s easier to convert the binary numbers to decimal numbers first -- otherwise, you’re likely to run out of digits!) ----------------------------------------
  • It's all relative, as they say. In acoustics, sound pressure level (SPL) is defined as: SPL = 20 log10 (P/Pref) dB Where: P is the sound pressure being measured, in N/m^2. Pref is the reference sound pressure, Pref = 2x10^-5 N/m^2. And sound power level is defined as: Sound Power = 10 log10 (P/Pref) dB Where: P is the estimated sound power of the unit under test, in Watts. Pref is the general sound power reference level, Pref = 10^-12 Watts. Mathematically, it is the reference level that determines whether a measured value is expressed as a positive or negative value when converted into dB. If we want to convert a voltage level into dB using a reference level of 1.0V, we use the following: 20 log (Voltage/1.0) dB There are at least two standard reference voltage levels used in pro audio: 0.775V (dBu) and 1.0V (dBV). Similarly, audio power measurements are expressed relative to 1 mW (dBm) or 1 Watt (dBW). If the measured voltage is 0.5 volts and a reference voltage of 1.0 V is used, the result will be -6.0 dBV. If the measured voltage is 2.0 volts, using the same reference, a value of +6.0 dBV is obtained. If we use the 0.775V reference, the results are -3.8 and +8.2 dBu for measured levels of 0.5 amd 2.0 volts, respectively. In short, if the measured parameter is less than the reference, the result will be negative. If it is greater than the reference, the result will be positive. A manufacturer may choose any method to describe their equipment. Unless you know what reference is being used, the results are somewhat meaningless.

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