Boolean algebra for beginner

[King Julian]

Hi again ..
me again ..

Although I can figure out the logic For the gates and Boolean law simplification etc. I do feel that I need to be more proficient in this topic as I find myself having to constantly go back and look at the laws and it’s applications etc..

Anyone got a nice ref/link to a tutorial that will help me with some of this “prerequisite” basic Boolean algebra and specifically it’s laws and application to work through.

I am finding a lot on the net , tried working through one or two , but still find myself a bit wanting... So asking here if that’s ok as I don’t want to digress too much away from the course while trying to become more proficient at this topic.

Thanks again In advance.
 

[Lozminda]

Hi

https://www.youtube.com/watch?v=2zRJ1ShMcgA

I had a quick skip through this vid, if anything it's a bit slow..

You do need some programming experience to do this course, and assuming you do have some programming experience would you not have some boolean algebra experience as part of that programming experience ? Perhaps there are some programming languages that don't use boolean algebra that i don't know of...(possible/likely ? hmmm)

I, Really, don't want to put you off, but if you're finding the boolean algebra difficult, the course going to get much harder, from chapters 4,5,6.

I re-itterate that you need some previous programming experience to complete this course.
quoting the beginning of the book under Courses

The book is completely self-contained, requiring only programming (in any language) as a prerequisite.
Thus, it lends itself not only to computer science majors, but also to computer-savvy students seeking to
gain a hands-on view of hardware architectures, operating systems, and modern software engineering in
the framework of one course.

There are people much wiser than I on this forum, they might have a suggestion or two

There's some ok stuff on the net, I googled "Boolean algebra for beginners"

Lozminda

[King Julian]

Thank you Lozminda ..much appreciated 👊🏽will use that link as well.
I also found a few other links and will update here after working through them.

interesting comment .. actually Many high level programming languages or rather levels of programming don’t really require Boolean algebra to write programs. My background for example is mainly business application programming levels etc and in reality these levels of Boolean algebra is hardly required in that world. I’ve even done assembler at the business application levels.

However , I am keen to work through this and don’t really mind The time frames it will take. I am not under any wrong impressions as to the amount of effort I have to put in etc..

Also , I don’t really have a time constraint as it is self study for me and a hobby of interest , so I don’t really mind having to branch off in order to cover some prerequisite basics etc ..  as a matter of fact I came across this course while researching some C learning I am busy with, which is therefore actually the result of a branch off from my C learning C .. 🙈😂...  

Thanks again and I think you can see just how much i will appreciate any help to push on further and cross bridges like these step by step 🙏🏽👊🏽.

[WBahn]

King Julian wrote

interesting comment .. actually Many high level programming languages or rather levels of programming don’t really require Boolean algebra to write programs. My background for example is mainly business application programming levels etc and in reality these levels of Boolean algebra is hardly required in that world. I’ve even done assembler at the business application levels.

I think you'll find it was required and that you did use it, you just didn't realize it for what it was. If you've every used an if() statement or a for(), do(), or while() loop, then you've used boolean expressions. A boolean expression is simply a mathematical statement that produces a boolean result, meaning a result that is either true or false.

For instance, in

if (x < y)
   x = 3 * y;

the expression x < y, is a boolean expression. More specifically, it is a relational expression, which is a subset of boolean expressions.

As another example, say you have a variable 'wages' and a category 'status'. You might have to encode something like: If the wages is greater than 80000 and the status is 'married-jointly', then the marginal tax rate is 22%.

You might write code that looks something like this:

if ( (wages > 80000) && (status.equals("married-jointly")) )
   taxRate = 0.22;

This is a logical expression (something) && (something else), which is another subset of boolean expression, and both (something) and (something else) are boolean expressions themselves.

If you've ever taken something like

if ( (5 < x) && (x < 10) )
   // code if x is between 5 and 10
else
   // code if x is outside 5 and 10

and changed it to

if ( (x <= 5) || (10 <= x) )
   // code if x is outside 5 and 10
else
   // code if x is between 5 and 10

Then you have done boolean algebra without realizing it.

[King Julian]

Wow WB .. thanks for that .. yes u are 100% correct if that’s the case 🤦🏽‍♂️

Maybe I am over complicating it .. 🙈

Anyway I am finding the K Map methods seems far easier ( for me ofcourse ) in terms of simplification which is where I wasn’t really too confident that I always have atleast some optimal results etc...  

[WBahn]

King Julian wrote

Wow WB .. thanks for that .. yes u are 100% correct if that’s the case 🤦🏽‍♂️

Glad I could shed some light.

Maybe I am over complicating it .. 🙈

Perhaps, but more likely simply a case of two things that are essentially the same appearing to be very different because of the superficial view that we have available to us. Once we have the information to look a bit further under the surface, we see the connections for what they are. And, of course, there's almost always more connections even further under the surface than we are able to view at any given point in our journey, so we often have to revisit things many times over a career.

Anyway I am finding the K Map methods seems far easier ( for me ofcourse ) in terms of simplification which is where I wasn’t really too confident that I always have atleast some optimal results etc...

K-maps definitely make simplifications easier once you know enough about how they work, or at least how to use them. Contrary to popular belief, though, they generally do not produce the "simplest" logic expressions, especially if we are looking at transistor-level implementations. In fact, they can actually explode the complexity of the logic, especially if XOR terms get involved.

The authors don't include simplification techniques, other then mentioning them in passing, because they aren't needed and most things that aren't needed are ignored or given some hand-wavy treatment. This is the consequence of having a course that is so unbelievably broad in scope that any depth that isn't essential is largely sacrificed. For their purposes, all that matters is that the implemented logic function correctly, no matter how inefficient the implementation might be.

[King Julian]

You guys have shed more light then u can imagine 👍🏽
Especially the part that highlights the importance of just understanding the concept and basic principles well enough at this stage to make it work ....

Thanks again , really appreciated