Boolean Algebra optimization question

Click For Summary
SUMMARY

This discussion focuses on the optimization of boolean expressions using the consensus theorem. The specific equation discussed is xy' + xz' + y'z, which simplifies to xz' + y'z. The user initially struggled to find a boolean algebra law for this optimization but later identified the consensus theorem as the solution. Additionally, the user noted that there are multiple forms of this theorem, including xy + x'z + yz = xy + x'z, corroborated by sources such as Wikipedia and academic texts.

PREREQUISITES
  • Understanding of boolean algebra principles
  • Familiarity with consensus theorem
  • Knowledge of Karnaugh maps (k-maps)
  • Basic skills in simplifying boolean expressions
NEXT STEPS
  • Study the consensus theorem in detail
  • Practice simplifying boolean expressions using k-maps
  • Explore different forms of boolean identities
  • Learn about other optimization techniques in boolean algebra
USEFUL FOR

This discussion is beneficial for students studying digital logic design, electrical engineers, and anyone involved in optimizing boolean expressions for circuit design.

FocusedWolf
Messages
81
Reaction score
0
Hi,

This is a question about a boolean "law" type behavior I've noticed in my homework a couple of times.

Basically i can't find a boolean algebra law that permits this optimization short of using a k-map.

bool.jpg


So I'm just wondering if theirs some way to optimize the one equation using just boolean algebra in order to get the second one (the output of the k-map).
 
Physics news on Phys.org
Nvm i found it in the solutions for that homework.

It's called the "consensus theorem"

where:

xy' + xz' +y'z =xz' + y'z

Had a feeling it was some obscure identity/law lol
 
Last edited:
OK apparently theirs two or more forms: xy + x'z + yz = xy + x'z

found this one in a book, and matched wikipedia.
 

Similar threads

Designing an XOR Gate from NOR Gates: Truth Tables and Boolean Algebra
  • · Replies 4 ·
Replies
4
Views
6K
Comp Sci Boolean simplification of a larger term?
  • · Replies 5 ·
Replies
5
Views
2K
Boolean Algebra Equivalencies: Can These Expressions Be Simplified?
  • · Replies 15 ·
Replies
15
Views
4K
Simplification of Boolean Expressions
  • · Replies 3 ·
Replies
3
Views
3K
Boolean algebra- cancellation property of addition
  • · Replies 2 ·
Replies
2
Views
4K
How Can You Simplify Boolean Expressions Using Only NOR Gates?
  • · Replies 2 ·
Replies
2
Views
2K
Boolean function - minterms - literals
  • · Replies 2 ·
Replies
2
Views
4K
Solving a SIMetrix Question for Digital Circuit Testing
  • · Replies 1 ·
Replies
1
Views
2K
Solving Boolean Algebra Qns: x+yz+x'y= (x+x')(x+y)+yz
  • · Replies 1 ·
Replies
1
Views
1K
How Can You Simplify This Boolean Expression Using Three Gates?
  • · Replies 1 ·
Replies
1
Views
2K