Do this R-2R ladder works?

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Do this R-2R ladder works? it requires less resistors and less tolerance, just 8bit +8bit equals to 16bit.

I know it need a complex logic to control such ladder, but i am not capable to figure it out yet.

Will it work? sound ok? I happen to get the word "R-2R" from google, and have no knowledge about electronics.
 

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Basically you designed a circuit that multiplies two unsigned 8 bit words while converting the product to analogue. For audio you would need to make it signed somehow, but on top of that, you can't convert any prime numbers greater than 256, nor composite numbers having a prime factor greater than 255 - or at least not accurately, you would have to round them to a near composite number with all prime factors smaller than 255.
 
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