What happens when you place a NOT gate before and after a NAND gate

In summary: ONTO THE REPORT WRITING.In summary, when a NOT gate is placed before and after a NAND gate, the resulting output is equivalent to an AND gate. This is because the NOT gate negates the values passed through it, and the NAND gate, being the negation of the AND gate, produces the opposite output. This can be explained using De Morgan's law, which states that the negation of a conjunction is the disjunction of the negations. Therefore, a NOT NAND gate is equal to an AND gate, and a NAND NOT gate is equal to an OR gate. This knowledge can be applied in designing logic circuits for various applications.
  • #1
dreadfear
6
0

Homework Statement


What happens when you place a NOT gate before and after a NAND gate


Homework Equations


Current Research(My own work):
NOT Gate: A NOT gate is also known as an inverter. It is a logic gate which implements a methodology best known in maths as Logical Negation. In other words a NOT gate takes whatever results that are passed through it, usually True or False(0 or 1) and negates them. A NOT gate only requires one value.

AND Gate: An AND gate is a logic gate which implements a methodolgy best known as logical conjunction. The logical conjunction linked with an AND gate appears when both values are true, thus returning the value of true. All other values return false. An AND gate requires 2 values to produce an output.

NAND Gate: A NAND gate follows the same principles as the afforementioned AND gate. However its results are effect by a NOT gate. According to the material above, a NOT gate negates values and an AND gate only returns true if both values are true. Using this we can deduce that the output of a NAND gate will be the exact opposite to those of an AND.

The Attempt at a Solution



Default NAND Gate:
INPUT
A B OUTPUT
0 0 1
0 1 1
1 0 1
1 1 0

Now a NOT gate placed infront of a NAND gate would invert the values being passed through it, but not the output. (This is where i start to get a little confused)

NOT NAND Gate:
INPUT
A B OUTPUT
1 1 1
1 0 1
0 1 1
0 0 0

Which is equal to an OR gate. (But I am not sure why?)

NAND NOT Gate:
INPUT
A B OUTPUT
0 0 0
0 1 0
1 0 0
1 1 1

Which is equal to an AND gate. Which kind of makes sense to me because if you put a negative and a negative together you get positive but once again I am not exactly sure.

Thanks in advance for any help, i appreciate it.
 
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  • #2
Hint: The Law of double negation.
 
  • #3
(logic) The statement that the negation of the negation of A implies A, for any proposition A.

Ok so NOT is a negation. And NAND is the negation of AND.

So NOT NAND(negation of the negation of A) = AND

NAND NOT (Negation of A Negated) = NAND?

Sorry I am still not getting this completely.
 
Last edited:
  • #4
dreadfear said:

Homework Statement


What happens when you place a NOT gate before and after a NAND gate


Homework Equations


Current Research(My own work):
NOT Gate: A NOT gate is also known as an inverter. It is a logic gate which implements a methodology best known in maths as Logical Negation. In other words a NOT gate takes whatever results that are passed through it, usually True or False(0 or 1) and negates them. A NOT gate only requires one value.

AND Gate: An AND gate is a logic gate which implements a methodolgy best known as logical conjunction. The logical conjunction linked with an AND gate appears when both values are true, thus returning the value of true. All other values return false. An AND gate requires 2 values to produce an output.

NAND Gate: A NAND gate follows the same principles as the afforementioned AND gate. However its results are effect by a NOT gate. According to the material above, a NOT gate negates values and an AND gate only returns true if both values are true. Using this we can deduce that the output of a NAND gate will be the exact opposite to those of an AND.

The Attempt at a Solution



Default NAND Gate:
INPUT
A B OUTPUT
0 0 1
0 1 1
1 0 1
1 1 0

Now a NOT gate placed infront of a NAND gate would invert the values being passed through it, but not the output. (This is where i start to get a little confused)

NOT NAND Gate:
INPUT
A B OUTPUT
1 1 1
1 0 1
0 1 1
0 0 0

Which is equal to an OR gate. (But I am not sure why?)

NAND NOT Gate:
INPUT
A B OUTPUT
0 0 0
0 1 0
1 0 0
1 1 1

Which is equal to an AND gate. Which kind of makes sense to me because if you put a negative and a negative together you get positive but once again I am not exactly sure.

Thanks in advance for any help, i appreciate it.

Does this link help?

http://en.wikipedia.org/wiki/Demorgan's_law

.
 
  • #5
No it doesn't but thanks anyway.

(It might but i don't understand how i can use it)

EDIT:
A & B = Inputs
O = Output
- = NOT
-(A^B) = NAND

NOT NAND = --(A^B) = (A^B) = AND (Is this correct?)

NAND NOT = -(A^B)-O = ? (I have absolutely no idea with this one, i don't even know how to set this one out.)
 
Last edited:
  • #6
Also, NOT is a unitary operation and NAND is a binary operations. Where before do you place your NOT gate?
 
  • #7
Where before do you place your NOT gate?

Sorry can you rephrase that?
 
  • #8
dreadfear said:
Where before do you place your NOT gate?

Sorry can you rephrase that?

Part of your problem statement says:

What happens when you place a NOT gate before ... a NAND gate

A NAND gate has 2 input and 1 ports. A NOT gate has 1 input and 1 output port. Draw the circuit diagram corresponding to your exact connection.
 
  • #9
Im not sure i can.

Because like you said, NOT gate has 1 input and 1 output. You can't connect 1 output to 2 inputs, it wouldn't work.

So a NOT NAND gate is impossible?

What about a NAND NOT?

I could see how that works. It takes the output value of the NAND, than negates it.

So a NAND NOT gate is equal to an AND gate.

Is this correct?
 
  • #10
yes.
 
  • #11
Haha damn my physics teacher. He told me this would be a good thing to right my report about, guess he included a trick question in there for me.

Thanks :) Now maybe i can get some sleep
 
  • #12
It might help further if you expand your truth table to 6 columns.

Code:
A' B' A  B  O  O'
      0  0  1
      0  1  1
      1  0  1
      1  1  0

O = not(A&B). Fill in A', B' and O' with the inverted values of A, B and O, respectively.

You should see that O' = not(A'orB'). This graphical method may be better for you to get used to than a tangle of words and symbols.
 

FAQ: What happens when you place a NOT gate before and after a NAND gate

1. What is a NOT gate?

A NOT gate, or inverter, is a logic gate that takes in one input and outputs the opposite value. For example, if the input is 0, the output will be 1, and if the input is 1, the output will be 0.

2. What is a NAND gate?

A NAND gate, short for NOT AND gate, is a logic gate that performs the opposite function of an AND gate. It will output 1 only when both inputs are 0, and will output 0 for all other combinations of inputs.

3. What happens when you place a NOT gate before a NAND gate?

When you place a NOT gate before a NAND gate, it is equivalent to using an AND gate. This is because the NOT gate will invert the input, and the NAND gate will then perform its usual function of outputting 0 only when both inputs are 1.

4. What happens when you place a NOT gate after a NAND gate?

When you place a NOT gate after a NAND gate, it is equivalent to using an OR gate. This is because the NAND gate will output 0 only when both inputs are 1, but the NOT gate will invert this to a 1. Therefore, the output will be 1 for all other combinations of inputs.

5. Can I use a NOT gate both before and after a NAND gate?

Yes, you can use a NOT gate both before and after a NAND gate. This would result in the same function as an XOR gate, where the output is 1 only when the inputs are different. However, this configuration is not commonly used as it can be achieved with a simpler logic gate, such as an XOR gate.

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