Can Boolean Logic Be Simplified to Use XOR Operations?

In summary, the boolean logic expression s=x'y'z+x'yz'+xy'z'+xyz can be simplified to s=x'y'z+x'yz'+xy'z', and the simplest expression is s=z(x xor y) + z'(x xor y).
  • #1
electronic engineer
145
3
let's consider this boolean logic experession:

s=x'y'z+x'yz'+xy'z'+xyz

can i simplify it to:

s=x'y'z+x'yz'+xy'z'

as xyz=1 where x,y,z in high logic(1)

what's the simplest expression?
 
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  • #2
You have 2 xor's

s=x'y'z+x'yz'+xy'z'+xyz

x'y'z + xyz = z(x'y' + xy) = z(x xor y)

x'yz' + xy'z' = z'(x'y + xy') = z'(x xor y)

add these up and go from there
 
Last edited:
  • #3
waht said:
You have 2 xor's

s=x'y'z+x'yz'+xy'z'+xyz

x'y'z + xyz = z(x'y' + xy) = z(x xor y)

x'yz' + xy'z' = z'(x'y + xy') = z'(x xor y)

add these up and go from there

x xor y= x'y+xy' that's right, but i don't think x'y'+xy=x xor y

are you sure from that?

thanks
 
  • #4
yea

xy +x'y' is just the complement of (x xor y)

(xy' + x'y)' = (x' + y)(x + y') = xy + x'y'
 
  • #5
s=x'y'z+x'yz'+xy'z'+xyz

x'y'z + xyz = z(x'y' + xy) = z(x xor y)'

x'yz' + xy'z' = z'(x'y + xy') = z'(x xor y)

so s=(z) xor (y) xor (z)
 

What is simple logic?

Simple logic is a branch of logic that focuses on understanding and analyzing arguments based on basic principles such as premises and conclusions. It involves identifying patterns of reasoning and evaluating the validity of arguments.

Why is simplifying simple logic important?

Simplifying simple logic is important because it allows for clearer and more efficient communication. By breaking down complex arguments into simpler forms, it becomes easier to understand and assess the validity of the argument.

What are some common techniques for simplifying simple logic?

Some common techniques for simplifying simple logic include identifying and eliminating irrelevant information, breaking down complex arguments into simpler ones, and using visual aids such as diagrams or flowcharts to represent the logic.

How can I improve my skills in simplifying simple logic?

To improve your skills in simplifying simple logic, you can practice identifying and analyzing arguments in everyday conversations or written texts. You can also study different logical fallacies and learn how to spot them in arguments.

Can simplifying simple logic be applied in other fields of study?

Yes, simplifying simple logic can be applied in various fields such as mathematics, computer science, and philosophy. It is a fundamental skill for critical thinking and problem-solving in any discipline.

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