Talk:Non-adjacent form

Latest comment: 3 years ago by Trex4321 in topic Merge proposal

Alternating signs paragraph

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The paragraph on alternating signs is not correct. Just consider the binary representation of decimal 9, being 1001, which is its unique NAF form.

It is however correct that the Booth Algorithm determines a signed digit representation where the signs of the non-zero digits alternate.

BUT the Booth algorithm does not generate a NAF representation! Take as an example a binary string with an isolated 1, say ... ..., which by the Booth Algorithm converts into ... ...

The original algorithm for converting a binary number into its equivalent and unique NAF form was given by Reitwiesner in 1960, but normally it is described by the following right-to-left algorithm:

Input:   in 2's complement
Output:  
 
for   to   do

  
 

end

— Preceding unsigned comment added by Kornerup (talkcontribs) 19:15, 8 February 2006 (UTC)Reply

Encoding the NAF of an m-bit number using m+1 bits

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The article currently states that "[b]cause every non-zero value has to be adjacent to two 0's, the NAF representation can be implemented such that it only takes a maximum of m + 1 bits for a value that would normally be represented in binary with m bits." Can someone provide more details on this "implementation"? 188.169.229.30 (talk) 19:39, 27 April 2013 (UTC)Reply

NAF example in Obtaining NAF

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While correcly labeling binary and NAF digits for one NAF digit more, it is not striking because zm − 2 is dropped. Also, how to show the zeroes?

   Input    E =    (em−1 em − 2e3 e2 e1 e0)2
   Output   Z = (zm zm−1 zm − 20 z2  0 z0)NAF

is intuitive, but flawed: z2 may be 0, allowing z3 to be non-zero. 84.63.77.35 (talk) 02:27, 31 May 2015 (UTC)Reply

Merge proposal

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It is proposed to merge Canonical signed digit into this page, they describe the same thing. 2001:4DD7:2E47:0:7285:C2FF:FE6C:992D (talk) 08:00, 12 July 2021 (UTC)Reply

The merge has been performed. Trex4321 (talk) 12:13, 8 August 2021 (UTC)Reply