How Can DeMorgan's Law Be Applied to Implement (A+B).(A+C) Using NAND Gates?

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The discussion revolves around implementing the expression (A+B)(A+C) using NAND gates and DeMorgan's Law. The original poster is struggling with the diagram and has attempted to simplify the expression but is confused about the next steps. A response clarifies that the double-negated form is not A.B + A.C and suggests expanding and simplifying the expression further. Additionally, guidance is provided on how to create and upload a circuit diagram. The conversation emphasizes the importance of understanding both the mathematical and visual aspects of the problem.
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Homework Statement


Hi
I am struggling with the diagram of this question. Can anyone help? I would have loaded my diagram but unsure how to do it. This is the question:

Starting with the following statement (A+B).(A+C), show how this can be implemented using NAND gates using DeMorgans law.



Cheers


Homework Equations





The Attempt at a Solution


After doubly negating, I obtained (A.B) + (A.C). And this is where I get stuck.
Please help. I have a deadline looming this week.
 
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Try to expand and then simplify the expression first.

ehild
 
Thanks for a response. I am okay with the maths but unsure about the actual diagram. Any pointers? Thanks.
 
The double-negated (A+B).(A+C) is not A.B+A.C.

If you do not know how to draw the diagram, see http://www.kpsec.freeuk.com/gates.htm. Copy the figures and construct the circuit from them.
If you do not know how to upload it into your post, click on "Go Advanced".

ehild
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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