Solve Boolean Algebra Homework

In summary, the expression ##cb' + ca'b + cabd + cad'## can be simplified to ##c## using the properties of boolean algebra, such as the distributive property and the identity A+A'B=A+B. Using a Karnaugh Map can also help to confirm the simplification.
  • #1
Kernul
211
7

Homework Statement


Simplify the expression ##cb' + ca'b + cabd + cad'##

Homework Equations


All the properties of boolean algebra.

The Attempt at a Solution


Here's how I did it:
$$cb' + ca'b + cabd + cad' = $$
$$c(b' + a'b + abd + ad') = $$
$$c(b' + a'b + a(bd + d')) = $$
$$c((a + a')b' + a'b + a(bd + (b + b')d')) = $$
$$c(ab' + a'b' + a'b + a(bd + bd' + b'd')) = $$
$$c(a(b' + bd + bd' + b'd') + a'b' + a'b) = $$
$$c(a(b'(d + d') + bd + bd' + b'd') + a'b' + a'b) = $$
$$c(a(b'd + bd' + bd + bd' + b'd') + a'b' + a'b) = $$
$$c(a(b'd + bd' + bd + b'd') + a'b' + a'b) = $$
$$c(a(b'(d + d') + bd' + bd) + a'b' + a'b) = $$
$$c(a(b'(d + d') + b(d' + d)) + a'b' + a'b) = $$
$$c(a(b' + b) + a'b' + a'b) = $$
$$c(a + a'b' + a'b) = $$
$$c(a + a'(b' + b)) = $$
$$c(a + a') = $$
$$c$$
Is all this correct? Was there a better and faster way to do it?
 
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  • #2
Have you checked your answer using a Karnaugh Map? That's a good way for you to check your answers in Boolean algebra manipulations. :smile:

(Hint -- I think you'll like what you find in your K-map)
 
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  • #3
It looks correct. Remember the identity A+A'B=A+B. It is very useful!
 
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1. What is Boolean algebra?

Boolean algebra is a type of mathematical logic that deals with binary values, usually represented as 0 and 1. It is used to analyze and simplify logical statements and is commonly used in digital electronics and computer science.

2. How do I solve Boolean algebra problems?

To solve Boolean algebra problems, you can use a variety of techniques such as truth tables, Karnaugh maps, and the laws of Boolean algebra. It is important to familiarize yourself with these methods and practice using them to solve different types of problems.

3. What are the basic laws of Boolean algebra?

The basic laws of Boolean algebra include the commutative law, associative law, distributive law, identity law, and complement law. These laws govern how logical statements can be manipulated and simplified.

4. Can I use Boolean algebra to simplify complex logical statements?

Yes, Boolean algebra is often used to simplify complex logical statements. By applying the laws of Boolean algebra, you can break down a statement into simpler terms and make it easier to understand and evaluate.

5. Are there any online resources or tools available to help with solving Boolean algebra homework?

Yes, there are many online resources and tools available to help with solving Boolean algebra homework. Some popular options include truth table generators, Karnaugh map solvers, and online tutorials and practice problems. It is important to use these resources responsibly and not rely on them too heavily.

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