Boolean Algebra (1 Viewer)

[acmilan]

Does anyone know the rules for Boolean algebra? From what ive seen from a trial paper this year its very useful in designing a circuit when a truth table is given

 

[sunny]

What sort of rules are you after?

 

[asdf]

SamD's book has a section on Boolean Algebra. I think he posted that chapter for free (atleast when i was doing SDD last year).

 

[Winston]

You should know about the De Morgan's Theorem, and also the Sums of Products and Products of Sums...

basically it's quite easy to draw a circuit from a given truth table...

lets take an example


A B C
0 0 0
0 0 1
0 1 0
0 0 1
.
.
.
etc...

i'm making this up, it's not suppose to make sense the above TT anyways

C is the output...

and whenever you see a 1 as the output, so for example one line of it is

A B C
1 0 1

since C's output is 1, this is what you do, for the inputs A and B, if ANY one of the inputs are 0, just NOT it, so that you would have A/B (/ indicates the bar on top of B, which is a NOT representation).

so lets make a bigger example

A B C
1 0 1 (A/B)
1 1 1 (AB)
0 1 1 (/AB)
0 0 0 (outputs aren't 1)
0 1 0 (outputs aren't 1)

when you got two inputs like this AB, it means (A times B) just like maths, and it's read as A AND B, and A OR B is read as A + B.

so now that you've got those AND equivalents from the truth table...(A/B), (AB), (/AB)

you just add them together, which is like OR'ing them

so A/B + AB + /AB

this is the Sums of Products

and basically there's quite a list of boolean algebra laws you can follow which i can't remember them all... haha you can pretty much do some simplification like taking common facotrs out etc...

However, from the above equation you can just draw it out as it is, because they cannot expect you to simplify it at all.

 

[jude_ess]

This site is really helpful in explaining the rules of De Morgan's Theorem

http://www.ee.surrey.ac.uk/Projects/Labview/boolalgebra/

I hope that helps!