Implementing a Logic Circuit with NAND & NOR Gates

In summary, the figure on the left shows the basic gate transformations. The yellow circles represent NOT operations that need to be added for the given gate type to stay equivalent to the others in the line. The important things to remember are: how to make a NOT gate out of either a NAND or a NOR, and if you move the NOT from output of a NAND or NOR to its input leads, the basic gate changes type (from AND to OR or from OR to AND). You can migrate the NOT circles along the continuous path of a circuit wire. Thus you can change their association from one gate to another. NOTs in series cancel in pairs.
  • #1
Sinister
33
0

Homework Statement



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Given the above circuit, implement the logic circuit with only NAND gates, and then one with only NOR gates.

Homework Equations



N/A

The Attempt at a Solution



I made a truth table but I'm pretty sure its wrong because I'm confused on how to implement the 'g' part of the circuit.

Is there an easier way of doing this?
 
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  • #2
Do you know how to form NOT gates from either a NAND gate or a NOT gate?
Do you know how to transform a NAND into a NOR and vice-versa?
Individual ANDs and ORs can obviously be transformed to NANDs and NORs if you tack a NOT gate on after them...

You can go through the circuit and make the conversions, then cancel all the redundant NOTs that appear.
 
  • #3
gneill said:
Do you know how to form NOT gates from either a NAND gate or a NOT gate?
Do you know how to transform a NAND into a NOR and vice-versa?
Individual ANDs and ORs can obviously be transformed to NANDs and NORs if you tack a NOT gate on after them...

You can go through the circuit and make the conversions, then cancel all the redundant NOTs that appear.


Is there no way to solve it mathematically?
I really don't like memorizing these types of concepts
 
  • #4
Sinister said:
Is there no way to solve it mathematically?
I really don't like memorizing these types of concepts

I suppose there must be, but it seems a lot of work to translate from a pictorial circuit to a mathematical form, then do the work, then convert back to a pictorial form. You can "do the math" visually right on the diagram by knowing a rather small number of "translations". Really, the method is practically algebraic in its methodology.
 
  • #5
Ok so I understand that not gate and the and gate form a NAND gate, and then the two NAND gates form another NAND gate. But then I get confused, and especially with part on the right hand side.
Care to explain the transformation?
 
  • #6
Sinister said:
Ok so I understand that not gate and the and gate form a NAND gate, and then the two NAND gates form another NAND gate. But then I get confused, and especially with part on the right hand side.
Care to explain the transformation?

In the following figure are the basic transformations. Read the lines of figures across the page; all the gate configurations on the same line are equivalent.

attachment.php?attachmentid=39775&stc=1&d=1318143131.gif


The yellow circles represent NOT operations that need to be added for the given gate type to stay equivalent to the others in the line. The important things to remember are:

1. How to make a NOT gate out of either a NAND or a NOR
2. If you move the NOT from output of a NAND or NOR to its input leads, the basic gate changes type (from AND to OR or from OR to AND). Thus if you remove the NOT circle from the tip of an NAND gate and place two such circles on the input leads, then change the gate type to an OR to preserve the the overall function.
3. You can migrate the NOT circles along the continuous path of a circuit wire. Thus you can change their association from one gate to another. This can be used to transform gate types (for example, taking the NOT circle from a NAND turns it into a AND, and the moved circle might cancel with one along, or at the other end of, the same wire). NOTs in series cancel in pairs.
 

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  • #7
Wow,
THANK YOU SO MUCH!
 

FAQ: Implementing a Logic Circuit with NAND & NOR Gates

1. How do NAND and NOR gates work?

NAND and NOR gates are basic logic gates that are used in digital electronics to perform logical operations. They both have two or more input terminals and one output terminal. The output of a NAND gate is only low (0) when all of its inputs are high (1), and the output of a NOR gate is only high when all of its inputs are low. In other words, NAND gates act as universal NOT gates, while NOR gates act as universal OR gates.

2. What is the advantage of using NAND and NOR gates in a logic circuit?

One advantage of using NAND and NOR gates in a logic circuit is that they can be used to implement any logical function. This means that instead of using multiple types of gates, such as AND, OR, and NOT gates, we can use just NAND or NOR gates to accomplish the same task. This simplifies the design process and reduces the number of components needed.

3. How do you implement a logic circuit using only NAND and NOR gates?

To implement a logic circuit using only NAND and NOR gates, you first need to determine the truth table for your desired logical function. Then, using De Morgan's laws, you can convert the logical function into an equivalent expression using only NAND or NOR gates. You can then use these expressions to design a circuit using only NAND or NOR gates.

4. What are the limitations of using NAND and NOR gates in a logic circuit?

One limitation of using NAND and NOR gates is that they are not as efficient as other types of gates, such as AND and OR gates. This is because they have more complex internal circuitry, which can result in slower operation and higher power consumption. Additionally, NAND and NOR gates are not as versatile as other gates, as they can only be used to implement specific logical functions.

5. Are there any real-world applications of logic circuits using NAND and NOR gates?

Yes, there are many real-world applications of logic circuits using NAND and NOR gates. These gates are commonly used in digital electronics, such as computers, calculators, and other electronic devices. They are also used in control circuits for industrial machinery, as well as in communication systems and signal processing applications.

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