XOR gate to XNOR gate boolean algebra

In summary, we discussed an XNOR gate with negated input and negated output, and how to achieve it using boolean algebra. We looked at the initial formula of ((AB')' + (A'B)')' and the expected output of AB + (AB)' and determined that they were not correct. Using De Morgan's Theorem, we simplified the expression to A'B'+AB, which is the correct expression for an XNOR gate with negated input and negated output.
  • #1
Ogakor
17
0
Xor gate with negated input and negated output.

The expected output is an XNOR gate. I can't get it with boolean algebra.

My initial formula is:
((AB')' + (A'B)')'

The expected output is:
AB + (AB)' right?

Please help me.
 
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  • #2
Is this your homework?
 
  • #3
thecritic said:
Is this your homework?

No, this was my seatwork and I didn't get the answer.
 
  • #4
must you show it with boolean algebra? I'd recommend, since this has only 2 inputs and 1 output, simply running through the 4 possible inputs and calculating the 4 possible outputs 1 at a time in a truth table.
 
  • #5
Ogakor said:
Xor gate with negated input and negated output.

The expected output is an XNOR gate. I can't get it with boolean algebra.

My initial formula is:
((AB')' + (A'B)')'

The expected output is:
AB + (AB)' right?

Please help me.
Neither of those expressions looks right to me.
 
  • #6
I'm pretty sure that we're talking about inverting only one of the inputs to the XOR gate.
So, instead of A XOR B, we would have A' XOR B

This would, in fact have the result as A XNOR B
 
  • #7
[(AB')+(A'B)]'

By De Morgan's Theorem
(AB')' • (A'B)'

Again by De Morgan's Theorem
(A'+B'') • (A''+B')

Simplify
(A'+B) • (A+B')

Multiply
A'A+A'B'+AB+BB'

*AA' and BB' are equal to 0

Therefore [(AB')+(A'B)]' = A'B'+AB
Hope this helps
 

1. What is the difference between an XOR gate and an XNOR gate in boolean algebra?

An XOR gate stands for "exclusive OR" and outputs a true value if one of its inputs is true, but not both. An XNOR gate stands for "exclusive NOR" and outputs a true value if both inputs are either true or false. Essentially, an XNOR gate is the inverse of an XOR gate.

2. How does an XOR gate and an XNOR gate work in boolean algebra?

An XOR gate works by comparing the inputs and producing an output of true if one of the inputs is true, but not both. An XNOR gate works by comparing the inputs and producing an output of true if both inputs are either true or false.

3. Can an XOR gate and an XNOR gate be represented using symbols in boolean algebra?

Yes, an XOR gate can be represented by the symbol ⊕ and an XNOR gate can be represented by the symbol ⊙ in boolean algebra.

4. Are XOR and XNOR gates the only gates that can be used in boolean algebra?

No, there are other gates such as AND, OR, NAND, and NOR gates that can also be used in boolean algebra. These gates have different logic operations and produce different outputs based on their inputs.

5. What are the practical applications of XOR and XNOR gates in boolean algebra?

XOR and XNOR gates are commonly used in digital circuits and computer hardware to perform logical operations. They are also used in encryption algorithms, data validation, and error detection systems.

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