Hi guys I attached a circuit image below and my equation . I was able to simplify it using Boolean algebra and the image is again attached. Would anybody think there is something wrong with my simplification?
Any help would be appreciated greatly thank you.

P.S. For my first equation the plus between the closing bracket on the left and the closing bracket on the right should be a plus with a circle around it. Word doesn't have this feature to allow me to do so.

Circuit:



Boolean Algebra:

 

Welcome to AAC!

You drew an XOR, but used OR in the first equation. Which is it?

 

To check if equation 3 is correct, try the circuit with A=0, B=1, C=1.
Do equation 3 and the circuit agree?

 

Hi guys I attached a circuit image below and my equation . I was able to simplify it using Boolean algebra and the image is again attached. Would anybody think there is something wrong with my simplification?
Any help would be appreciated greatly thank you.

P.S. For my first equation the plus between the closing bracket on the left and the closing bracket on the right should be a plus with a circle around it. Word doesn't have this feature to allow me to do so.

Circuit:

View attachment 124503

Boolean Algebra:
View attachment 124504

You indicated that the + sign in the first equation is supposed to be XOR, but then you proceeded to forget that and treated it like an OR. This is why you want to use proper notation. If you can't find the proper symbolic operator, then just use XOR.

BTW: Word does have that symbol. It's called "circled plus". It's in the Insert Symbol dialog well down the list (code 2295).

One of the nice things about most engineering fields is that the correctness of an answer can be determined from the answer itself. You came up with the claim that the output is always the opposite of A. So set A=LO and see if there is anyway to make the output LO using the other two inputs. Then set A=HI and see if there is anyway to make the output HI using the other two inputs.

Well, if A is LO, then the top input to the XOR is equal to B and that means that, regardless of the other input, changing B will make x toggle. So clearly B has an effect and the answer is wrong.

Get in the habit of checking your own work - as an engineer or other technical professional, you will generally not have someone around to do so (there's a reason why they are paying YOU to solve the problem!). So now is the time to develop and hone those skills.