Digital logic - Boolean algebra simplification problem

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SUMMARY

The discussion focuses on simplifying the Boolean expression (A+B')(B+C) to its minimal form. The initial expansion yields AB + AC + B'C, but the correct simplification is AB + B'C. The key to eliminating the AC term lies in recognizing that when B is true, A must also be true, while if B is false, C must be true. This understanding of Boolean algebra principles, particularly the use of the identity (B+B') = 1, is crucial for simplification.

PREREQUISITES
  • Understanding of Boolean algebra principles
  • Familiarity with logical operators (AND, OR, NOT)
  • Experience with algebraic manipulation of expressions
  • Knowledge of simplification techniques in digital logic design
NEXT STEPS
  • Study Boolean algebra simplification techniques
  • Learn about Karnaugh maps for visual simplification
  • Explore the application of De Morgan's Theorems in logic circuits
  • Investigate digital logic design tools like Logisim or Quartus
USEFUL FOR

This discussion is beneficial for students of digital logic design, computer engineers, and anyone interested in mastering Boolean algebra for circuit optimization.

theBEAST
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Homework Statement


Simplify (A+B')(B+C)

The Attempt at a Solution


I first expanded it and got
= AB + AC + B'B + B'C
= AB + AC + B'C

Turns out the solution is AB + B'C (according to an online source). How do we get rid of the AC term?
 
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On examining the expression, you can see ...
If B is true, then for the expression to be true, the only condition that need be met is that A is true, and it doesn't matter what C is.

If B is false, then for the expression to be true all we need is that C is true, it doesn't matter what A is.

Just as in algebra you can multiply any term by 1 and you don't change its value, then in Boolean algebra you can multiply a term by true and you change nothing.

For example, (B+B') is true, and it's always true.

AB + AC(B+B') + B'C

expand this out, then simpify the result
 

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