Digital logic - Boolean algebra simplification problem

In summary, the expression given is (A+B')(B+C) and the attempt at simplifying it led to AB + AC + B'C. However, the correct solution is AB + B'C as shown by an online source. To get rid of the AC term, it was observed that if B is true, then A must also be true for the expression to be true, and if B is false, then C must be true. This is similar to multiplying a term by 1 in algebra, where the value remains unchanged. Therefore, the final simplified expression is AB + B'C.
  • #1
theBEAST
364
0

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?
 
Physics news on Phys.org
  • #2
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
 

1. How is Boolean algebra used in digital logic?

Boolean algebra is used in digital logic to represent and manipulate logical expressions, which are used to design and analyze digital circuits. These expressions are based on the basic logical operations of AND, OR, and NOT, and can be simplified using Boolean algebra rules to reduce the complexity of a circuit.

2. What is the purpose of simplifying Boolean algebra expressions?

The main purpose of simplifying Boolean algebra expressions is to reduce the number of logic gates and inputs required in a digital circuit, which in turn reduces the cost and complexity of the circuit. Simplification also helps in improving the overall efficiency and speed of the circuit.

3. How do you simplify a Boolean algebra expression?

To simplify a Boolean algebra expression, you can use the rules and laws of Boolean algebra, such as the distributive law, De Morgan's law, and the complement law. These rules allow you to manipulate the expression by combining terms and eliminating redundant or unnecessary elements until you reach the most simplified form.

4. What are the benefits of using Boolean algebra simplification in digital logic?

Using Boolean algebra simplification in digital logic has several benefits, including reducing the cost and complexity of circuits, improving circuit efficiency and speed, and making the design process more organized and systematic. It also allows for easier troubleshooting and debugging of digital circuits.

5. Are there any tools or software available for Boolean algebra simplification?

Yes, there are several tools and software programs available for Boolean algebra simplification, such as truth table generators, Karnaugh map solvers, and logic minimization software. These tools can help in simplifying complex Boolean algebra expressions and can be useful for digital logic design and analysis.

Similar threads

  • Engineering and Comp Sci Homework Help
Replies
5
Views
1K
  • Set Theory, Logic, Probability, Statistics
Replies
21
Views
1K
  • Precalculus Mathematics Homework Help
Replies
1
Views
1K
  • Engineering and Comp Sci Homework Help
Replies
4
Views
947
  • Introductory Physics Homework Help
Replies
2
Views
2K
  • Precalculus Mathematics Homework Help
Replies
4
Views
881
  • Precalculus Mathematics Homework Help
Replies
7
Views
1K
  • Engineering and Comp Sci Homework Help
Replies
5
Views
1K
  • Engineering and Comp Sci Homework Help
Replies
5
Views
1K
  • Introductory Physics Homework Help
Replies
7
Views
1K
Back
Top