How do I simplify this boolean function using the rules of boolean algebra?

Click For Summary
SUMMARY

The discussion focuses on simplifying the boolean function CA + CB + B'A to CB + B'A using boolean algebra rules. The user is struggling to demonstrate the equivalence of both expressions algebraically, despite confirming their equality through a truth table. The key takeaway is the importance of applying boolean algebra laws, such as the Consensus Theorem, to simplify expressions effectively.

PREREQUISITES
  • Understanding of boolean algebra principles
  • Familiarity with boolean functions and expressions
  • Ability to construct and interpret truth tables
  • Knowledge of the Consensus Theorem in boolean algebra
NEXT STEPS
  • Study the Consensus Theorem in boolean algebra
  • Practice simplifying boolean expressions using Karnaugh maps
  • Learn about De Morgan's Theorems and their applications
  • Explore advanced boolean algebra techniques for circuit design
USEFUL FOR

This discussion is beneficial for students studying digital logic design, electrical engineering students, and anyone interested in mastering boolean algebra for circuit simplification.

Ownaginatious
Messages
37
Reaction score
0
Okay, so I'm stuck at a step of a much bigger problem where I have to simplify a boolean function.

Homework Statement



Here is where I'm stuck, I have to change the left hand side to the right hand side. How do I prove this with the rules of boolean algebra?

CA + CB + B'A = CB + B'A

Homework Equations



0199541454.boolean-algebra.1.jpg


The Attempt at a Solution



The above is as far as I've gotten (as I said, this was taken from a bigger problem).

Can someone please show me the steps that will change the left hand side of the equation to the right? According to truth tables, they are infact equal.
 
Physics news on Phys.org
This appears wrong as the expression you wrote implies A+B=B, which is not true for a complete truth table.
 
Well, according to this truth table, it's right:

http://img170.imageshack.us/img170/3023/truth.png

I can't figure out how to prove this algebraically though.
 
Last edited by a moderator:

Similar threads

Can you help me solve this Boolean algebra problem?
  • · Replies 1 ·
Replies
1
Views
2K
MHB Prove that the statement is always true using the rules of boolean algebra
  • · Replies 9 ·
Replies
9
Views
2K
Undergrad What Are the Axioms of Fuzzy Logic and How Do They Extend Boolean Algebra?
  • · Replies 7 ·
Replies
7
Views
3K
Calculating Probabilities in a Double-Elimination Tournament
  • · Replies 2 ·
Replies
2
Views
2K
Comp Sci Boolean simplification of a larger term?
  • · Replies 5 ·
Replies
5
Views
2K
Boolean algebra -Sum of products form - theorem
  • · Replies 1 ·
Replies
1
Views
6K
Is This Simplified Boolean Expression Correct?
  • · Replies 2 ·
Replies
2
Views
2K
How to know if a certain number is a don't care in KMAP
  • · Replies 11 ·
Replies
11
Views
2K
Boolean Algebra Proof Statement
  • · Replies 9 ·
Replies
9
Views
5K
Problems in manipulating these 4 radical equations
  • · Replies 8 ·
Replies
8
Views
2K