# [sdiy] Digital is more analog than analog... and it has 319 dB headroom...

Tom Wiltshire tom at electricdruid.net
Sun Mar 3 11:57:36 CET 2024

```This is splitting hairs. The point he's making is that there's bags more accuracy available for a digital system to model a situation than an analog one. In that sense, the digital is the better analog (in the other sense). And that's plainly true.

It's a reasonable point, but I don't think it really goes that far: "Modern computers are really powerful"? Nice work, Sherlock!

TBH, the whole analog vs digital thing is pretty stale after 40 years.

> On 3 Mar 2024, at 09:11, cheater cheater via Synth-diy <synth-diy at synth-diy.org> wrote:
>
> Also, btw, I thought someone would catch that without it being
> mentioned, but 300 dB isn't even the right number, even if we follow
> the bizarro logic that the bozo in the video is following.
>
> This is from the second link:
>
>> Let’s forget about the decimal point for now, because that only
>> scales a number up or down and has nothing to do with its
>> accuracy. It’s the 53-bits that is important, so let’s get a feel for that.
>> 53-bits represents a difference of 9,000,000,000,000,000:1. Yeah,
>> that’s 9 quadrillion to one, from the smallest to the largest quantity,
>> or a whopping, no, staggering, 319db
>
> you heard that right. according to this clown, scaling a number up and
> down doesn't have anything to do with how precise of a quantity you
> can describe. You can describe a cup of sugar? and you can also
> describe 1000 cups of sugar? Doesn't matter - 1000 cups of sugar are
> just 1 scaled up by a thousand, so being able to describe 1 cup of
> sugar isn't any more precise than being able to describe a sack of
> sugar. according to Mark Barton, at least. enjoy your pancakes with a
> full burlap sack of sugar dumped into the skillet.
>
> in reality, that's not how floating point numbers work. they have the
> ability to scale the significant by an exponent *exactly because* that
> improves accuracy by orders of magnitude. specifically by 308 orders
> of magnitude up, and 308 orders of magnitude down, so in total 616
> orders of magnitude. without using the exponent field, the smallest
> positive number you can describe with a float is
> 1.00000011920928955078125. with using the exponent field, the smallest
> positive number you can describe is a 0, then a decimal point, then
> 307 zeros, then a two, and then some other digits. that's incredibly
> more precise. the bozo in this video didn't do his basic research on
> floating point numbers and now he's giving talking head interviews
> about the topic. this guy can't even get his bullshit straight.
>
> If you wanted to really calculate the "dynamic range" of floating
> point numbers you would calculate it this way:
>
> 1. what is the smallest number representable as a 64-bit float?
> answer: 2.2250738585072014*10^-308 (call that V1)
>
> 2. what is the largest number representable as a 64-bit float? answer:
> 1.7976931348623158*10^308 (call that V2)
>
> 3. calculate the ratio: V2 / V1 = 0.80792515178... * 10^616
>
> 4. convert to decibels: dB = 20 * log10 (V2 / V1) = 20 * log10
> (0.80792515178 * 10^616) = 20 * (log10(0.80792515178) + log10 (10^616))
> = 12318 dB.
>
> Twelve thousand decibels of dynamic range. Another ridiculous number.
> And that's BEFORE dithering. This shows you how insipid it is to even
> think in this manner.
>
> This hopefully brings the point that you shouldn't be talking about
> what floating point numbers will or won't do unless you really *do*
> know, have checked the technical references, have experience and
> check your estimations at every step.
>
>
>
>
>
> On Sun, Mar 3, 2024 at 8:53 AM cheater cheater
> <cheater00social at gmail.com> wrote:
>>
>>> It DOES keep the noise and distortion from building up and becoming audible after dozens, hundreds, or even billions of MAC-type operations
>>
>> you're wrong. i can take a full scale 64 bit floating point signal and
>> get you that noise and distortion in 1 multiplication, or even one
>>
>> i thought we were making fun of the disinformation, not stuffing it in
>> a pipe and smoking it.
>>
>>
>> On Sun, Mar 3, 2024 at 4:38 AM Ben Bradley via Synth-diy
>> <synth-diy at synth-diy.org> wrote:
>>>
>>> The "300dB" dynamic range of "digital" totally misses the point. It
>>> has nothing directly to do with DR. It DOES keep the noise and
>>> distortion from building up and becoming audible after dozens,
>>> hundreds, or even billions of MAC-type operations on each 64-bit
>>> floating-point number. Surely he knows that, but it may be harder to
>>> describe and is "less impressive" than the dynamic range of lots of
>>> bits.
>>>
>>> On Sat, 2 Mar 2024 at 14:40, Gordonjcp <gordonjcp at gjcp.net> wrote:
>>>>
>>>> On Sat, Mar 02, 2024 at 08:19:29PM +0100, cheater cheater via Synth-diy wrote:
>>>>> I'll leave this here:
>>>>>
>>>>>
>>>>> and supplementary material:
>>>>>
>>>>> https://cherryaudio.com/news/flashback-friday-mark-barton-on-analog-and-modern-digital-synthesis
>>>>>
>>>>> make sure to hit the bong extra hard before you look at any of that...
>>>>
>>>> As an exercise for the student, try to work out what sort of signal levels would be involved in "300dB signal to noise ratio".
>>>>
>>>> --
>>>> Gordonjcp
>>>>
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>
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