Hi again,
If you use "code" wraps you can write out the logic statements so that they can be read more easily.
Your first expression came out to:
Code:
_ _ _
A*C+B*C
which can also be written as:
_ _
C*(A+B)
What you need to do is go over the NAND circuit again because your expression for that circuit does not look correct. When you get the correct expression from this particular circuit it should be the exact same as the AND OR circuit.
However, with Demorgan in mind what we can do is redraw the NAND circuit using INVERTERS and AND gates rather than NAND gates. The final NAND gate (on the far right) is thus turned into an AND gate with inverters on the input and on the output, and the two other NAND gates are turned into just AND gates. Then looking at the final AND gate with both it's inputs and it's outputs inverted, we can then draw it as an OR gate with no inverters. This makes the circuit look *exactly* like the circuit with the AND and OR gates, and this happens without doing any math at all. This is really the essence of using Demorgan rather than simply Boolean Algebra, but the Boolean Algebra simplifies too this way as expected through Demorgan.
We can draw that final AND gate (with inverters on it's inputs and output) as an OR gate because of Demorgan's which in other words states that:
"If we invert all inputs and outputs we can invert the logical connective and remove all inverters".
Since the final AND gate has all it's inputs and outputs inverted, we can remove all of the inverters and change the gate to an OR gate because the invert of an AND gate is an OR gate. That's the beauty of Demorgan.