# Full Adder Sum Formula (Logic)

1. May 19, 2009

### King

Hi,
I've been trying to work out the formula for the sum for the full adder logic, however have come across a gap which I don't know how to fill.
S = (¬A.¬B.C) + (¬A.B.¬C) + (A.¬B.¬C) + (A.B.C)
S = ¬A.(¬B.C + B.¬C) + A.(¬B.¬C)
S = ¬A.(B $$\oplus$$ C) + A.( do not know what to do at this point to reach the next stage
S = (A $$\oplus$$ B) $$\oplus$$ C

Does anyone know how to get to that last statement?

Thanks for any help.

Last edited: May 19, 2009
2. May 19, 2009

### Staff: Mentor

It's probably easiest to draw a Karnaugh map for the function, and use that to help your intuition in the reduction. Have you drawn a K-map for this yet?

3. May 20, 2009

### King

Nope. I have never used one before.

Edit: How come this received a warning? This isn't homework or coursework. It's just studying.

4. May 20, 2009

### Staff: Mentor

Studying is coursework. Even if it's for self-study, it belongs in the Homework Help forums, and needs to follow the rules here. You can check out the Rules link at the top of the page for clarification.

The K-map is a great tool for helping you visualize logic reduction. Here's an intro to get you started -- there are lots of other learning resources for K-maps on the web:

http://en.wikipedia.org/wiki/Karnaugh_map

.

5. May 21, 2009

### King

That doesn't make sense since every thread in these forums is about help to understand something, so one could always link it to a course since there are courses for everything, and thus everything should therefore be in the Homework Help forums. But anyway...

Does anyone know how to solve this without the K-map since I don't really have colouring pencils to create this diagram, just a pen? Also, how would one solve this algebraically?

6. May 21, 2009

### Defennder

Why do you need coloured pencils for the Karnaugh map?