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AR# 14220

LogiCORE - Twos Complementer Core: Why is the output width created equal to (input width + 1)?

Description


General Description: 
Why does the Twos Complementer core always create an output width that is one bit greater than the input width? (If the input width is "n", then output width will always be "n+1".)

Solution


The Twos Complementer accepts signed input. If the input width is "n", then the range of signed numbers the core can accept is: 
 
-(2^(n-1)) to +(2^(n-1)-1) 
 
The extra bit on the output is needed when the input is the lower limit of the range. 
 
For example
 
For n=8, the valid input range is -128 to +127 ("10000000" to "01111111").  
 
If the input is -128, the complement must be to +128. This requires the extension of a single bit to obtain a valid sign bit -> "010000000" (9-bits needed).
AR# 14220
Date Created 08/29/2007
Last Updated 05/20/2014
Status Archive
Type General Article