Three bit addition consists of adding the two digits in the addends a, b, and the carry from the column to the right c_{in} to produce sum and c_{out}
The Boolean expressions for these two outputs are:
sum =
(~a · ~b · c_{in}) + (~a · b· ~c_{in}) + (a · ~b · ~c_{in}) + (a· b · c_{in})
c_{out} =
(~a· b · c_{in}) + (a · ~b· c_{in}) + (a · b · ~c_{in}) + (a· b · c_{in})
Which can be seen in the Truth Table:
INPUT  OUTPUT  

PROBLEM:
Verify that the above equations can be derived from this table. The following may help you:
INPUT  OUTPUT  Term  




 



 



 



 



 



 



 (~a· b · c_{in})  



 




INPUT  OUTPUT  Term  




 



 



 



 



 



 (~a · ~b · c_{in})  



 



 




Fill in the remainder of the white rows yourself.
CS1104 Main Page
Last Updated 2002/02/17
© L.Heath 2000, updated by J.A.N. Lee.