Bit-resolution decrease for internet

Radium wrote:
> 44100 X 16 X 2 = 1,441,200
>
> 44100 X 1/88200 X 2 = 1

Why won't you respond to my postings asking you how you intend to represent
and use fractional bits?

Ben
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Ben Pope wrote:

> Radium wrote:
> 
>>44100 X 16 X 2 = 1,441,200
>>
>>44100 X 1/88200 X 2 = 1
> 
> 
> Why won't you respond to my postings asking you how you intend to represent
> and use fractional bits?

What is wrong with fractional bits?  A decimal digit is worth 3.3 bits.

There are many computations that use fractional bits.

Sampling isn't usually one, though.

-- glen

glen herrmannsfeldt wrote:
> Ben Pope wrote:
>
>> Radium wrote:
>>
>>> 44100 X 16 X 2 = 1,441,200
>>>
>>> 44100 X 1/88200 X 2 = 1
>>
>>
>> Why won't you respond to my postings asking you how you intend to
>> represent and use fractional bits?
>
> What is wrong with fractional bits?  A decimal digit is worth 3.3 bits.

Implementation is a fairly large problem.  I'm fairly sure a transistor is
either logically "off" or logically "on".  If you had 1/88200 of a
transistor, I doubt it would work, so physically you cannot have fractional
bits.  If you had 1/88200 of a logical bit, how do you determine the state
of that bit?  it has 1.0000something states.  What is a fraction of a state?
Does it even mean anything if it could be represented?

The point is you cannot have a fraction of a bit.  A bit is the atomic unit
of digital computation, there is nothing smaller as it cannot represent
state, without state you have nothing.

You can have fractional values represented in binary but thats not the same
thing.  It still uses an integer number of bits.

> There are many computations that use fractional bits.

Not really.  You can't measure something with 3.3 bits, can you?  You can't
create a machine that can represent 2^3.3 (~9.85) states.

> Sampling isn't usually one, though.

Nothing can use fractional bits, they just don't exist in a physical world
(somebody will pull out an anology in quantum physics now, but I don't see
its relevance in todays computing environment, besides, you can still can't
have a fraction of a qubit)

Ben
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I'm not just a number. To many, I'm known as a String...

Radium wrote:

> 44100 X 16 X 2 = 1,441,200
> 
> 44100 X 1/88200 X 2 = 1

I assume that you mean 1/88200 to represent "bit resolution". You
misunderstand. The formula calls for resolution measured in bits. For
CDs, that is 16 bits. The step size represented by one count out of 16
bits is 1/65,536 of the maximum peak-to-peak level that the converters
can handle. Step size is not directly related to bit rate.

Everyone is entitled to an opinion. Some opinions are worth more than 
others. Yours seem to be worth very little.

Jerry
-- 
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������

Ben Pope wrote:

   ...
\
> Nothing can use fractional bits, they just don't exist in a physical world
> (somebody will pull out an anology in quantum physics now, but I don't see
> its relevance in todays computing environment, besides, you can still can't
> have a fraction of a qubit)
> 
> Ben

Not only bits, but digits. You can buy a 3 1/2 digit DVM. Digits and
bits are measures of precision. When the actual precision is not an
integer times an integer power of the number base, fractions come into
the representation. Physical realization isn't needed to give the
representation meaning. Or were you just pulling my leg?

Jerry
-- 
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������

Jerry Avins wrote:
> Ben Pope wrote:
>
>    ...
> \
>> Nothing can use fractional bits, they just don't exist in a physical
>> world (somebody will pull out an anology in quantum physics now, but I
>> don't see its relevance in todays computing environment, besides, you
>> can still can't have a fraction of a qubit)
>>
>> Ben
>
> Not only bits, but digits. You can buy a 3 1/2 digit DVM. Digits and
> bits are measures of precision. When the actual precision is not an
> integer times an integer power of the number base, fractions come into
> the representation. Physical realization isn't needed to give the
> representation meaning. Or were you just pulling my leg?

A bit is not a measure of precision.  It is a state machine with 2 states.
The "value" of the bit is completely irrelevant in this discussion.

From Radiums calculations, he appears to want to store 88200 samples in one
bit, you can't.  That would require splitting the bit into 88200 "chunks",
you can't.

You can't implement a unit of storage with non-integer number of states in
the digital domain.  And you simply can't have a unit of storage with less
than 2 states, otherwise it will contain no information (if you have one
level you know what it will be and is therefore completely deterministic, if
you have zero levels you don't have anything) and will therefore be
completely useless to you.

I realise that you can bunch a load of bits together (a byte, two bytes, a
word, whatever), then order them - together the (ordered) set of states will
provide an integer (since you are either in one state or another, no
half-states) index which you could multiply by some pre-determined
fractional value that each bit represents, to give an overall value that can
represent a fraction.  That I'm happy with.

A 3� digit DVM or display is not a good example here.

Ben
-- 
A7N8X FAQ: www.ben.pope.name/a7n8x_faq.html
Questions by email will likely be ignored, please use the newsgroups.
I'm not just a number. To many, I'm known as a String...

Ben Pope wrote:

> Jerry Avins wrote:
> 
>>Ben Pope wrote:
>>
>>   ...
>>\
>>
>>>Nothing can use fractional bits, they just don't exist in a physical
>>>world (somebody will pull out an anology in quantum physics now, but I
>>>don't see its relevance in todays computing environment, besides, you
>>>can still can't have a fraction of a qubit)
>>>
>>>Ben
>>
>>Not only bits, but digits. You can buy a 3 1/2 digit DVM. Digits and
>>bits are measures of precision. When the actual precision is not an
>>integer times an integer power of the number base, fractions come into
>>the representation. Physical realization isn't needed to give the
>>representation meaning. Or were you just pulling my leg?
> 
> 
> A bit is not a measure of precision.  It is a state machine with 2 states.
> The "value" of the bit is completely irrelevant in this discussion.

I think your range of allowed use is entirely too restrictive. I use a 
bit in my lathe, and after one broke in two, I used half a bit. Howard 
Hughes made a fortune selling bits to oil-well drillers, and repairing 
them. [retracting tongue from cheek] Even taking the restricted meaning 
of binary digit, digits are parts of numbers. Orders if magnitude have 
their place, but it is sometimes important to use in-between values. 
Hence 3.5 digit meters.

> From Radiums calculations, he appears to want to store 88200 samples in one
> bit, you can't.  That would require splitting the bit into 88200 "chunks",
> you can't.

Radium is an opinionated ass. That he's cock sure doesn't make hid 
drivel worth considering. Don't expect rationality. If he were capable 
of hearing other people, this discussion would be long over.

> You can't implement a unit of storage with non-integer number of states in
> the digital domain.  And you simply can't have a unit of storage with less
> than 2 states, otherwise it will contain no information (if you have one
> level you know what it will be and is therefore completely deterministic, if
> you have zero levels you don't have anything) and will therefore be
> completely useless to you.

a system capable of distinguishing 16 states is said to be a 4-bit 
system. One that can have 32 states is a 5-bit system. How would you 
characterize the information capacity in bits of a system that can have 
12 states? I get 3.585 bits. That's log2(12).

> I realise that you can bunch a load of bits together (a byte, two bytes, a
> word, whatever), then order them - together the (ordered) set of states will
> provide an integer (since you are either in one state or another, no
> half-states) index which you could multiply by some pre-determined
> fractional value that each bit represents, to give an overall value that can
> represent a fraction.  That I'm happy with.
> 
> A 3� digit DVM or display is not a good example here.

Why not?

Jerry
-- 
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������

Jerry Avins wrote:
> Ben Pope wrote:
>> A bit is not a measure of precision.  It is a state machine with 2
>> states. The "value" of the bit is completely irrelevant in this
>> discussion.
>
> I think your range of allowed use is entirely too restrictive.

Not given the context.

> I use a
> bit in my lathe, and after one broke in two, I used half a bit. Howard
> Hughes made a fortune selling bits to oil-well drillers, and repairing
> them. [retracting tongue from cheek]

Yes, well done.  So anyway, back to the discussion:

> Even taking the restricted meaning
> of binary digit, digits are parts of numbers.

Thats nice.  A bit is still only capable of 2 states.  A binary digit is
still capable of 2 states (0 and 1)

> Orders if magnitude have
> their place, but it is sometimes important to use in-between values.
> Hence 3.5 digit meters.

A 3.5 digit meter is designed to display fractions.  It is used to display a
"1" (or nothing) in the most significant digit, this also must be an integer
since x.5 digit meters do not have the possiblity of point (decimal or
otherwise) to the left of the � digit.

>> From Radiums calculations, he appears to want to store 88200 samples in
>> one bit, you can't.  That would require splitting the bit into 88200
>> "chunks", you can't.
>
> Radium is an opinionated ass. That he's cock sure doesn't make hid
> drivel worth considering. Don't expect rationality. If he were capable
> of hearing other people, this discussion would be long over.

But he's not alone in being unable to grasp the fact that a bit has a finite
amount of storage, namely two states.  You seem to be struggling also,
mostly becuase you seem to have forgotten what we are talking about.

>> You can't implement a unit of storage with non-integer number of states
>> in the digital domain.  And you simply can't have a unit of storage with
>> less than 2 states, otherwise it will contain no information (if you
>> have one level you know what it will be and is therefore completely
>> deterministic, if you have zero levels you don't have anything) and will
>> therefore be completely useless to you.
>
> a system capable of distinguishing 16 states is said to be a 4-bit
> system. One that can have 32 states is a 5-bit system. How would you
> characterize the information capacity in bits of a system that can have
> 12 states? I get 3.585 bits. That's log2(12).

Yes, but you cannot implement it with a state register containing 3.585 bits
can you?  You'd need 4.  So what you have to say still doesn't demonstrate
the possiblilty of fractional bits.  Merely your inability to distinguish
the mathematical domain from real life.

>> I realise that you can bunch a load of bits together (a byte, two bytes,
>> a word, whatever), then order them - together the (ordered) set of
>> states will provide an integer (since you are either in one state or
>> another, no half-states) index which you could multiply by some
>> pre-determined fractional value that each bit represents, to give an
>> overall value that can represent a fraction.  That I'm happy with.
>>
>> A 3� digit DVM or display is not a good example here.
>
> Why not?

You're not even talking about the same thing as me, thats why.  It's an
example of something completely different.

Ben
-- 
I'm not just a number. To many, I'm known as a String...

Ben Pope wrote:
> A 3.5 digit meter is designed to display fractions.

A 3.5 digit meter is NOT designed to display fractions.

Ben
-- 
A7N8X FAQ: www.ben.pope.name/a7n8x_faq.html
Questions by email will likely be ignored, please use the newsgroups.
I'm not just a number. To many, I'm known as a String...

Ben Pope wrote:

> Jerry Avins wrote:
> 
>>Ben Pope wrote:
>>
>>>A bit is not a measure of precision.  It is a state machine with 2
>>>states. The "value" of the bit is completely irrelevant in this
>>>discussion.
>>
>>I think your range of allowed use is entirely too restrictive.
> 
> 
> Not given the context.

That's probably true, but I had given up trying to educate Radium, and
so broadened the context. What do you make of the statement that every
bit added to a storage unit doubles its capacity. If a five-bit word
holds 32 items and a four-bit word only 16, isn't it true that the fifth
bit is "worth" 16 items all by itself? :-)

> 
>>I use a
>>bit in my lathe, and after one broke in two, I used half a bit. Howard
>>Hughes made a fortune selling bits to oil-well drillers, and repairing
>>them. [retracting tongue from cheek]
> 
> 
> Yes, well done.

Thanks.

>  So anyway, back to the discussion:
> 
> 
>>Even taking the restricted meaning
>>of binary digit, digits are parts of numbers.
> 
> 
> Thats nice.  A bit is still only capable of 2 states.  A binary digit is
> still capable of 2 states (0 and 1)

Absolutely. but the notion of a bit isn't limited to the number of
states it can have. "Bit" is also used as a measure of capacity. Not all
capacities are powers of two.

>>Orders if magnitude have
>>their place, but it is sometimes important to use in-between values.
>>Hence 3.5 digit meters.
> 
> 
> A 3.5 digit meter is designed to display fractions.  It is used to display a
> "1" (or nothing) in the most significant digit, this also must be an integer
> since x.5 digit meters do not have the possiblity of point (decimal or
> otherwise) to the left of the � digit.

Not so. I once had a meter that could display one, zero, or blank in the
MSD place. Zero was used when the decimal point was to the left of it on
the lowest range.

>>>From Radiums calculations, he appears to want to store 88200 samples in
>>>one bit, you can't.  That would require splitting the bit into 88200
>>>"chunks", you can't.
>>
>>Radium is an opinionated ass. That he's cock sure doesn't make hid
>>drivel worth considering. Don't expect rationality. If he were capable
>>of hearing other people, this discussion would be long over.
> 
> 
> But he's not alone in being unable to grasp the fact that a bit has a finite
> amount of storage, namely two states.  You seem to be struggling also,
> mostly becuase you seem to have forgotten what we are talking about.

We agree about what a one-bit storage element can hold. We differ about
what a bit, as a unit of capacity can signify. I claim that a count of
bits (and more generally, digits of any base) can signify an information
capacity, and an integer isn't requires in that service.

I agree also that my comment digressed from the attempt to disabuse
Radium. I had given up on that and thought I was having fun in the
spirit of a Fred Allen radio skit long before commercial television. A
party in Egypt was looking for the remains of King Tut. Two people in
different places claimed to have found the sarcophagus almost 
simultaneously. Allen objected: "There can't be two Tuts!" "Oh no?" his
foil (Don the Beachcomber) answered. "Haven't you ever heard of
tut-tut?" It seemed funny at the time, but his delivery is better than
mine.

>>>You can't implement a unit of storage with non-integer number of states
>>>in the digital domain.  And you simply can't have a unit of storage with
>>>less than 2 states, otherwise it will contain no information (if you
>>>have one level you know what it will be and is therefore completely
>>>deterministic, if you have zero levels you don't have anything) and will
>>>therefore be completely useless to you.
>>
>>a system capable of distinguishing 16 states is said to be a 4-bit
>>system. One that can have 32 states is a 5-bit system. How would you
>>characterize the information capacity in bits of a system that can have
>>12 states? I get 3.585 bits. That's log2(12).
> 
> 
> Yes, but you cannot implement it with a state register containing 3.585 bits
> can you?  You'd need 4.  So what you have to say still doesn't demonstrate
> the possiblilty of fractional bits.  Merely your inability to distinguish
> the mathematical domain from real life.

I'm not claiming that fractional bits are physically possible. I'm
trying to establish their usefulness as a measure of capacity.


>>>I realise that you can bunch a load of bits together (a byte, two bytes,
>>>a word, whatever), then order them - together the (ordered) set of
>>>states will provide an integer (since you are either in one state or
>>>another, no half-states) index which you could multiply by some
>>>pre-determined fractional value that each bit represents, to give an
>>>overall value that can represent a fraction.  That I'm happy with.
>>>
>>>A 3� digit DVM or display is not a good example here.
>>
>>Why not?
> 
> 
> You're not even talking about the same thing as me, thats why.  It's an
> example of something completely different.

Yes. I'm sorry.

The moral of this story is, never say "never" Above all, never give
advice. Well, no. What I was really getting at, even if obliquely, is
that there are often oblique ways to look at things things that open
many categorical statements to question.

Jerry
-- 
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������