Boolean Algebra

  • Thread starter Kernul
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  • #1
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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?
 

Answers and Replies

  • #2
berkeman
Mentor
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9,157
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
ehild
Homework Helper
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It looks correct. Remember the identity A+A'B=A+B. It is very useful!
 
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