How To Implement This Function With 2 Input Nand

In summary, the conversation discusses how to implement a function with two input NANDs and transform it into a Sum of Products (SOP) form. The final equation is shown to be equal to \overline{({AB})({CD})} and the use of NANDs as inverters is suggested to get the necessary inputs.
  • #1
transgalactic
1,395
0
Default How To Implement This Function With 2 Input Nand..
(+) =XOR

F(w,x,y,z)=(w'+x'+y')(+)xyz

i tried to :

F(w,x,y,z)=(w'+x'+y')(+)xyz=(w'+x'+y')' *(xyz) + (w'+x'+y')(xyz)'=
=(wxy)(xyz)+(w'+x'+y')(x'+y'+z')
..
..
in the end i get
=wxyz+w'x'+w'y'+w'z'+x'+x'y'+x'y'+y'+y'z'+y'z'

what to do know?
how to transform implement it with a two input line NANDs
?
 
Physics news on Phys.org
  • #2
Well, the word NAND should scream Sum of Products (SOP), so try to get your function to that point, then you can modify it further. After playing around with your function, you should get something like:

[tex]F = \overline{x} + \overline{y} + (\overline{w})(\overline{z}) + wxyz[/tex]

(Keep in mind that [tex]A+AB = A[/tex]; your final equation doesn't take that into account).

I'm going to show you another useful proof:

[tex]\overline{ABCD} = \overline{A}+\overline{B}+\overline{C}+\overline{D} = (\overline{A}+\overline{B})+(\overline{C}+\overline{D}) = \overline{AB}+\overline{CD} = \overline{(\overline{AB})(\overline{CD})} [/tex]

The function is also equal to (through DeMorgan):
[tex]F = \overline{xy ( \overline{ \bar{w} \bar{z} })( \overline{wxyz}) }[/tex]

Use the proof above on that form of F. Use the proof above to get [tex]\overline{(wxyz)}[/tex], too. Use NANDs as inverters to get w' and z'.
 
  • #3
I think There is a mistake it should be [tex] \overline{AB}+\overline{CD} = \overline{({AB})({CD})} [/tex]
 

1. How does a 2-input NAND function work?

A 2-input NAND function is a logic gate that takes in two inputs and produces an output based on the following truth table:

Input A Input B Output
0 0 1
0 1 1
1 0 1
1 1 0

This means that the output will only be 0 when both inputs are 1, otherwise the output will be 1.

2. How do I implement a 2-input NAND function in my circuit?

To implement a 2-input NAND function, you will need to use two transistors and connect their outputs to a single output wire. The two inputs will be connected to the base of each transistor, and the emitters of the transistors will be connected to ground. The collectors of the transistors will be connected to the output wire. This setup will produce a 2-input NAND function.

3. What is the purpose of using a 2-input NAND function?

A 2-input NAND function is commonly used in digital logic circuits as it can perform the logical operation of a NOT gate combined with an AND gate. This allows for more complex logic operations to be built using only NAND gates.

4. Can I implement a 2-input NAND function using other logic gates?

Yes, a 2-input NAND function can also be implemented using other logic gates such as NOR gates or combinations of AND and NOT gates. However, using NAND gates is more efficient as it requires fewer components and can simplify the circuit design.

5. Are there any limitations to using a 2-input NAND function?

One limitation of using a 2-input NAND function is that it can only take in two inputs. If you need to perform a logical operation on more than two inputs, you will need to use multiple NAND gates or a different type of logic gate. Additionally, the accuracy of the output may be affected by variations in the transistors used in the circuit.

Similar threads

  • Engineering and Comp Sci Homework Help
Replies
3
Views
5K
  • Engineering and Comp Sci Homework Help
Replies
4
Views
2K
  • Engineering and Comp Sci Homework Help
Replies
5
Views
2K
  • Engineering and Comp Sci Homework Help
Replies
1
Views
1K
  • Engineering and Comp Sci Homework Help
Replies
1
Views
5K
  • MATLAB, Maple, Mathematica, LaTeX
Replies
4
Views
1K
  • Introductory Physics Homework Help
Replies
3
Views
954
  • Engineering and Comp Sci Homework Help
Replies
7
Views
2K
  • Engineering and Comp Sci Homework Help
Replies
4
Views
26K
  • Engineering and Comp Sci Homework Help
Replies
3
Views
803
Back
Top