Is Multiplying Terms the Correct Approach in Boolean Algebra Simplification?

[James889]

Hi,

I have the following boolean function.

$$\overline{bd} + bd + acd$$

To minimize this function is the solution to simply multiply the first two terms by
$$(a+\overline{a})(c+\overline{c})$$ ?

 

[LCKurtz]

The first two terms give 1 to the whole expression is 1.

 

[Mark44]

By "minimize this function" do you mean to write it as simply as possible?

If so, it seems to me that you eliminate the first two terms, since they will have opposite truth values, which makes their union/conjunction always true.

 

[James889]

Hi,

I need to realize that function using a multiplexer (1 of 8), I am not sure if canceling terms is the right way to do "it"

 

[LCKurtz]

Hi,

I need to realize that function using a multiplexer (1 of 8), I am not sure if canceling terms is the right way to do "it"

The way to realize that function is to tie your output to V_c.

 

[James889]

Im supposed to do it using shannon expansion

 

[LCKurtz]

Im supposed to do it using shannon expansion

Well, I don't claim to be the local expert about Shannon expansions and multiplexers, so what I am proposing is a suggestion; you can figure out if you can use it. What about writing:

$$\overline{bd} + bd + acd = \overline b + \overline d + bd + acd$$

Now since the first term is the only one missing a d, multiply it by
$$(d+\overline d)$$

Then do a Shannon expansion on d. I think you will still come out with a multiplexed implementation of "1". Are you sure you have stated the problem correctly?