Re: Full adder

Posted by joobcode on Feb 06, 2013; 11:29am
URL: http://nand2tetris-questions-and-answers-forum.52.s1.nabble.com/Full-adder-tp4026235p4026238.html


Well bad algebra I knew already ;-)

Where I write good I mean I have tested the circuit and it is correct for cout.

Cout:
 
A'BC+AB'C + ABC'+ABC good
Apply the distributive law.
C(A'B+AB') + A(BC'+BC) good
Given that x.x' = 1 I can reduce the 1st term:
C  + A(BC'+BC) bad, am I miss applying here?

So applying x.x'=1 to the term C(A'B+AB') causing the circuit design it yields to break. Really not sure why? Is it because I am negating A an B variables from that term altogether?

Strangely if I do this it works:

cout = A'BC+AB'C + ABC'+ABC
Expand ABC
A'BC+AB'C +ABC'+ABC+ABC+ABC
Using x+x'=1 for 1st and 4th, 2nd and 5th, 3rd and 6th term.
BC+AC+AB

So far I am at a loss to understand why I must expand before I can reduce with x+x'=1 in this example. Till now just applying the rules like x+x'=1, x'x = 0 etc have worked well.