- Thread starter
- #1

For a timing diagram - synthesize the function $f$(x1,x2,x3) in the simplest sum of products form.

So I have a picture of this timing diagram, which I can't really show on here unless i physically took a picture and uploaded it, but it's really irrelevant because I know I have the correct truth table, so hopefully we can work with that.

So my Truth Table reads:

So now I know I have

Which means I have:

So I need to put this function in the

So here it goes.. (

.... x2 x3

.. 00 01 11 10

x1 0[1) 0 1 0]

.. 1[0 1 0 (1]

So my question Is what now? How should I group all these 1s? Just group each of them by themselves? And if so, How do I read off what is going on here?

Would I read it like this ?

Thanks for your time.

If this is something you can't explain or think I should just read more up on, please let me know, because I can take constructive criticism. I just want to make sure I know how to do these.

So I have a picture of this timing diagram, which I can't really show on here unless i physically took a picture and uploaded it, but it's really irrelevant because I know I have the correct truth table, so hopefully we can work with that.

So my Truth Table reads:

- x1 x2 x3 | f
- 0 0 0 | 1
- 0 0 1 | 0
- 0 1 0 | 0
- 0 1 1 | 1
- 1 0 0 | 0
- 1 0 1 | 1
- 1 1 0 | 1
- 1 1 1 | 0

So now I know I have

**$f$(x1,x2,x3) = \(\displaystyle \sum\)m(0,3,5,6)**Which means I have:

**x!x2!x3! + x1!x2x3 + x1x2!x3 + x1x2x3!**So I need to put this function in the

**simplest sum of products form**.. So I'm assuming i need to minimize the function that I just got above?*If*I am on the right track- then I now need to use a**to find the minimization.***K-Map*So here it goes.. (

**This is my K-Map**).... x2 x3

.. 00 01 11 10

x1 0[1) 0 1 0]

.. 1[0 1 0 (1]

So my question Is what now? How should I group all these 1s? Just group each of them by themselves? And if so, How do I read off what is going on here?

Would I read it like this ?

**x1!x2!x3! + x1x2!x3 + x1!x2x3 + x1x2x3!**?Thanks for your time.

If this is something you can't explain or think I should just read more up on, please let me know, because I can take constructive criticism. I just want to make sure I know how to do these.

Last edited: