# Quick question on boolean algeba

1. Nov 28, 2009

### 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
$$(a+\overline{a})(c+\overline{c})$$ ?

2. Nov 28, 2009

### LCKurtz

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

3. Nov 28, 2009

### Staff: Mentor

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.

4. Nov 28, 2009

### James889

Hi,

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

5. Nov 28, 2009

### LCKurtz

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

6. Nov 28, 2009

### James889

Im supposed to do it using shannon expansion

7. Nov 29, 2009

### LCKurtz

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?