# Boolean algebra basics

Discussion in 'Math' started by Airmax, Feb 17, 2008.

1. ### Airmax Thread Starter New Member

Feb 17, 2008
3
0
Hey there guys,

I have just started studying electronics at uni and have started boolean algebra. I am having a little problem simplifying the expressions as most people seem to. I am aware of the laws but I am having troubles understanding how to move and manipulate variables to be able to apply the laws.

A.B + B.C + A'.C = Z

With this expression I just dont know where to start. What Im not sure of is the rules to moving the variables around. If someone could break this expression down to step by step sections it would be a great help.

Thanks

Trev

2. ### S_lannan Active Member

Jun 20, 2007
247
2
okay. i don't blame you it all looks like crap until you actually see what it means in logic.

This form of expression is called a sum of products.

Basically i see it as this

A AND B
OR
B AND C
OR
NOT A AND C

graphically ?
look at the attachment

This equation is taken straight from a truth table

It's saying this and this... OR this and this.... OR this and this - will make the Z go high.

File size:
3.7 KB
Views:
65
3. ### Dave Retired Moderator

Nov 17, 2003
6,960
144
The first thing you should look for is common factors. Lets look at you equation for example:

A.B + B.C + A'.C = Z

And lets look at just the first two terms:

A.B + B.C

It should be clear that B is a common factor to both terms, so simplified:

A.B + B.C = B(A + C)

Conversely, from your first equation you could have looked at the second two terms:

B.C + A'.C

Again, it should be clear that C is a common factor, so:

B.C + A'.C = C(B + A')

Therefore there are two equally valid simplifications for this equation:

B(A + C) + A'.C = Z

A.B + C(B + A') = Z

These are equally valid simplifications of the original expression for two reasons:

1) The implement the same output for a given set of inputs.
2) They are implemented using the same number of gates.

When looking at common factors, look for identities to remove gates from the expression. And you should also look at apply DeMorgan's theorems, to more advanced problems, particularly when you need to look at implementing a function using universal; gates. If you've only just started studying Boolean algebra, you come onto these in due course.

Dave

4. ### Airmax Thread Starter New Member

Feb 17, 2008
3
0
Thanks heaps guys, your advice has been greatly appreciated and things are starting to make more sense.

Cheers !!

Trev

Nov 17, 2003
6,960
144
6. ### aliashar86 Active Member

Nov 23, 2006
71
0
good reply given by "Dave" .

ok u also if could get "Digital fundamental by Floyd" it could also help u alot. also as this subject is mostly connected to ur practical work so try to plot the expression using the gates.

for multiplication: AND