Full adder

Posted by joobcode on Feb 05, 2013; 8:56pm
URL: http://nand2tetris-questions-and-answers-forum.52.s1.nabble.com/Full-adder-tp4026235.html

Rather than using halfadders I wanted to see what a simplified canonical representation of the full adders truth table would yield.

As there are 2 outputs, I assumed that I would need to build 2 seperate C.R's. One for Sum output and one for the Carry?

I get this:

a   b   c    car     sum    carCR    sumCR
0   0   0     0        0      
0   0   1     0        1                  A'B'C
0   1   0     0        1                  A'BC'
0   1   1     1        0       A'BC
1   0   0     0        1                  AB'C'
1   0   1     1        0       AB'C
1   1   0     1        0       ABC'
1   1   1     1        1       ABC      ABC

CR sum =  A'B'C+A'BC'+AB'C'+ABC
CR car  =  A'BC+AB'C+ABC'+ABC

Why does this simplification not work?

Carry:
A'BC+AB'C + ABC'+ABC good
C(A'B+AB') + A(BC'+BC) good
C               + AB           bad

What am I missing?