How to Convert AND/OR Circuits to NAND/NAND Using Only NAND and NOT Gates?

[mathrocks]

I have to make a circuit using only NAND and NOT gates to drive a 7 segment LED. My problem is that after I make the truth table and draw the karnaugh maps I of course end up with a AND/OR circuit...how exactly can I convert the AND/OR to a NAND/NAND. Also, how can I break up the 3 and 4 input AND gates to 2 input NAND gates.

I really need help with this, I've been racking my brain trying to figure this out.

Thanks alot!

 

[Cliff_J]

Ok, think of this. Take a simple NAND truth table.

NOT the output. You get ________

NOT the two inputs. You get ________

A 3 input AND can be 2 inputs into an AND with output fed into another AND along with the third input. A four input, use three ANDs. Etc.

If you draw it out I believe its that simple.

Cliff

 

[ravenprp]

Hello,

It seems like you are facing a common challenge when working with logic circuits. However, do not worry, there are a few steps you can follow to convert your AND/OR circuit to a NAND/NAND circuit.

First, let's review the basic properties of NAND and NOT gates. A NAND gate is equivalent to an AND gate followed by a NOT gate. This means that you can replace any AND gate with a NAND gate followed by a NOT gate. Similarly, a NOT gate is equivalent to a NAND gate with both inputs connected together. This means that you can replace any NOT gate with a NAND gate with both inputs connected together.

Now, to convert your AND/OR circuit to a NAND/NAND circuit, you will need to follow these steps:

1. Replace all AND gates with NAND gates followed by a NOT gate.
2. Replace all OR gates with NAND gates with both inputs connected together.
3. Use De Morgan's theorem to convert the NAND gates into NOR gates.
4. Use De Morgan's theorem again to convert the NOR gates into NAND gates.
5. Repeat steps 3 and 4 until you have a circuit with only NAND gates.

To break up the 3 and 4 input AND gates into 2 input NAND gates, you can use the distributive property. For example, a 3 input AND gate can be broken up into two 2 input NAND gates by connecting one input of each NAND gate to one of the inputs of the AND gate, and the other input of each NAND gate to the remaining input of the AND gate. You can follow a similar approach for 4 input AND gates.

I hope this helps you with your circuit. Remember to double-check your circuit after converting it to make sure it functions correctly. Good luck and don't give up!