Quantization Error

On Tue, 29 Sep 2015 06:55:30 +0000, glen herrmannsfeldt wrote:

> Tim Wescott <seemywebsite@myfooter.really> wrote:
>> On Mon, 28 Sep 2015 19:19:50 -0400, robert bristow-johnson wrote:
>  
> (snip)
> 
>>> he was saying "1s complement" (which is the same as "sign-magnitude"),
>>> in which if the truncation is done by masking off the bits, it will
>>> always "round toward zero".  but i dunno anybody other than IEEE-754
>>> that is doing sign-magnitude.
>  
> (snip)
> 
>> One's compliment and sign-magnitude are not the same: <https://
>> en.wikipedia.org/wiki/
>> Signed_number_representations#Signed_magnitude_representation>.
> 
> Ones complement is what you get exclusive oring all the non-sign bits
> with the sign bit. In the sense Robert was using it, the result is the
> same.

I was not arguing with his results, I was just picking nits with his 
declaration that one's compliment was the same thing as sign-magnitude.

They're not.

-- 

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

On 9/29/15 2:55 AM, glen herrmannsfeldt wrote:
> Tim Wescott<seemywebsite@myfooter.really>  wrote:
>> On Mon, 28 Sep 2015 19:19:50 -0400, robert bristow-johnson wrote:
>
> (snip)
>
>>> he was saying "1s complement" (which is the same as "sign-magnitude"),
>>> in which if the truncation is done by masking off the bits, it will
>>> always "round toward zero".  but i dunno anybody other than IEEE-754
>>> that is doing sign-magnitude.
>
> (snip)
>
>> One's compliment and sign-magnitude are not the same:<https://
>> en.wikipedia.org/wiki/
>> Signed_number_representations#Signed_magnitude_representation>.
>

ooops, you're right.  i knew that, but i misremembered.


> Ones complement is what you get exclusive oring all the non-sign
> bits with the sign bit. In the sense Robert was using it, the
> result is the same.

no, i fucked it up, Glen.  i conflated 1's comp with sign magnitude.

the difference between 1's comp and 2's comp is the number 1.

>
> If someone inverted all the bits of a bit representation, would
> you consider it the same enough?
>
>> One's compliment denotes negative numbers by changing the sense of _all_
>> the bits.

1's comp as both +0 and -0.  and 1's comp need not worry about the 
asymmetric overflow from negating 0x8000.  that was probably the only 
68000 programming trick i learned from Ralph Muha's code at Kurzwiel. 
very useful trick (with the expense of a tiny bit of deterministic error 
that you might be able to account for somewhere else in the signal 
chain) that saves a few instructions.

>  Sign-magnitude just sets the sign bit.

and that's what i was thinking and i conflated it with 1's complement. 
that was a mistake and i should have known better.

thanks for the support, Glen.  but i goofed it up a little.


-- 

r b-j                  rbj@audioimagination.com

"Imagination is more important than knowledge."

On 9/29/15 4:14 PM, Tim Wescott wrote:
> On Tue, 29 Sep 2015 06:55:30 +0000, glen herrmannsfeldt wrote:
>
>> Tim Wescott<seemywebsite@myfooter.really>  wrote:
>>> On Mon, 28 Sep 2015 19:19:50 -0400, robert bristow-johnson wrote:
>>
>> (snip)
>>
>>>> he was saying "1s complement" (which is the same as "sign-magnitude"),
>>>> in which if the truncation is done by masking off the bits, it will
>>>> always "round toward zero".  but i dunno anybody other than IEEE-754
>>>> that is doing sign-magnitude.
>>
>> (snip)
>>
>>> One's compliment and sign-magnitude are not the same:<https://
>>> en.wikipedia.org/wiki/
>>> Signed_number_representations#Signed_magnitude_representation>.
>>
>> Ones complement is what you get exclusive oring all the non-sign bits
>> with the sign bit. In the sense Robert was using it, the result is the
>> same.
>
> I was not arguing with his results, I was just picking nits with his
> declaration that one's compliment was the same thing as sign-magnitude.
>

and i had a very plain nit.

> They're not.


of course, you're correct, Tim.



-- 

r b-j                  rbj@audioimagination.com

"Imagination is more important than knowledge."