How do I convert CC-NOT gates to OR operators?

In summary, the conversation discussed the use of Fredkin Gates and their ability to recreate AND, OR, and XOR gates. While the first two were successfully recreated, the speaker was struggling to figure out how to recreate XOR using only Fredkin Gates. However, it was later mentioned that by using only C-NOT, CC-NOT, and NOT gates, it is possible to recreate all three gates. The speaker also received help in understanding how to recreate OR using these gates.
  • #1
khkwang
60
0
Fredkin Gates are supposed to be universal. So far I've gotten AND, OR and NOT out of them but I can't figure out XOR. Any help?

I know that A XOR B = (A AND NOT B) OR (B AND NOT A), but trying to recreate that with Fredkin Gates is not very elegant... is that the only way?

Edit: I guess I can't change the title of my thread...

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nvm this bottom part of this post, it's been solved already.

According to Feynman Lectures in Computing, by using only C-NOT, CC-NOT and NOT gates we can recreate AND, OR and XOR gates.

I understand how to create AND and XOR, but I can't work out the OR. I spent a good few hours pondering and trying out different truth tables but I just don't get it. Can anyone demonstrate a way?
 
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  • #2
If you have AND and NOT, then NOT ( (NOT (INPUT1)) AND (NOT (INPUT2)) ) = ((INPUT1) OR (INPUT2))
 
  • #3
Ahh so simple. Can't believe I forgot something so basic. Thanks, you actually helped me clear up a whole other question as well.
 
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Related to How do I convert CC-NOT gates to OR operators?

1. How do I convert a CC-NOT gate to an OR operator?

To convert a CC-NOT gate to an OR operator, you can use De Morgan's laws. First, invert the inputs of the CC-NOT gate and connect them to a NAND gate. Then, invert the output of the NAND gate to get the OR operator.

2. Can I use a different logic gate to convert CC-NOT to OR?

Yes, you can also use a NOR gate to convert CC-NOT to OR. In this case, you would invert the inputs of the CC-NOT gate and connect them to a NOR gate. The output of the NOR gate will be the OR operator.

3. What is the difference between CC-NOT and OR?

CC-NOT and OR are both logic gates that have two inputs and one output. However, the main difference between them is the output. CC-NOT produces the inverse of the input, while OR produces a true output if either or both of the inputs are true.

4. Can I convert more than one CC-NOT gate to OR at the same time?

Yes, you can convert multiple CC-NOT gates to OR operators simultaneously. This can be done by connecting the inverted inputs of the CC-NOT gates to a single NAND or NOR gate, and then inverting the output of the gate to get the OR operator.

5. Are there any limitations to converting CC-NOT to OR?

One limitation of converting CC-NOT to OR is that the inputs of the CC-NOT gate must be binary (0 or 1). If the inputs are not binary, the conversion may not produce the desired result. Additionally, the output of the OR operator will always be true if either or both of the inputs are true, unlike the CC-NOT gate which produces the inverse of the input.

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