Drawing circuits with NAND gates

In summary, to implement the circuit using only NAND gates and no NOT gates, we can wire a NAND gate to act as an inverter. This allows us to create the expression $f$(w,x,y,z) = x*y + w*x + \bar{y}*\bar{z}. The variables y and z are necessary for the circuit to function properly.
  • #1
shamieh
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A cheap way to implement this circuit is to use only NAND gates. Draw the circuit diagram for the lowest cost implementation using these gates. (reminder: you can wire a NAND gate such that it acts like an inverter).

$f$(w,x,y,z) = \(\displaystyle x*y + w*x + \bar{y}*\bar{z}\)

My solution:
View attachment 1448 Will this work?
 

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  • #2
shamieh said:
Will this work?
Close, but the problem statement says you can use only NAND gates, in particular, no NOT gates. However, NOT is easily expressible through NAND.

logic-gates1.png
 
  • #3
Wow the fact that you got that your drew that diagram on here is awesome lol. But where is the y y and z z coming from? aren't those unnecesarry?
 
  • #4
shamieh said:
But where is the y y and z z coming from? aren't those unnecesarry?
I don't understand the question, "Where are they coming from?". Do you know where x is coming from? What's the difference between x and y?
 
  • #5
Nevermind, I see now.
 

FAQ: Drawing circuits with NAND gates

What are NAND gates?

NAND gates are logic gates that perform the operation of a logical "not and" operation. This means that the output of a NAND gate will be true (or 1) only when both of its inputs are false (or 0).

How do you draw circuits with NAND gates?

To draw a circuit with NAND gates, you first need to understand the logic behind the NAND gate. Then, you can use symbols and diagrams to represent the NAND gate and its inputs and outputs. Finally, you can use logic diagrams to connect multiple NAND gates together to create more complex circuits.

What are the advantages of using NAND gates in circuit design?

NAND gates have several advantages in circuit design, including their simplicity and versatility. They can be used to create all other logic gates, making them a fundamental building block in digital circuits. They also have a simpler physical construction compared to other gates, making them more reliable and less prone to errors.

Can you give an example of a circuit drawn with NAND gates?

Yes, one example of a circuit drawn with NAND gates is a basic SR latch. This circuit uses two NAND gates to store and remember a single bit of information, making it a fundamental component in memory circuits.

Are there any limitations to using NAND gates in circuit design?

While NAND gates have many advantages, they also have some limitations. One limitation is their inability to perform certain functions, such as multiplication or division. Additionally, using too many NAND gates in a circuit can lead to complex and difficult to understand designs. It is important to carefully consider the specific needs of a circuit before deciding to use NAND gates in its design.

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