Electronics - Logic Gates Truth Tables

[qwerty]

I have a question about truth tables for the logic gates. I am given the truth table, I have to work out what the circuit would look like and what the function of the logic gate is ... like

 

I have to find out :

 

x = a.b.c + a.b + c

 

that was just an example.. Now this is the truth table i am given:

 

A B C Output

0 0 0 0

0 0 1 1

0 1 0 1

1 0 0 1

0 1 1 0

1 0 1 0

1 1 0 0

1 1 1 0

 

 

Would anyone be able to tell me the function of this truth table, or tell me the diagram of the setup of the combined logic gates, i think it SHOULD be used with AND OR and NOT gates combined.

[YT2095]

a.b.c you could use a 3 input And gate (or combine 2 ands and take the output of one and feed that to the input of another to make a tripple input type.

 

a.b+c a.b are just ANDed and the output is taken to one input of an OR gate, the remaining input of that OR gate is for c.

 

there are your 2 halves, now the out put of each half is then fed into the input of a single OR gate.

 

I`de send you a diagram but my camera server`s not working, so text is the only way I can explain.

 

btw, it`s not the convention to have 2 a b c inputs, it would be d e f instead

[qwerty]

thanks YT,

 

would you or anyone else have any idea how i could tell by looking at that truth table, the circuit or components that would make up that truth table?

 

is it just a guess and check way or is there a better way to do it. I am pretty sure it only consists of and or and not gates. thanks

[YT2095]

your truth table looks to be a tripple input XOR gate. this can be a single device or made up of a couple of 2 input XORs.

[Ego]

It's been a while since I've done these, but I think I can help you.

There are two ways to do it: you can go straight to the diagram or you can try to optimize the function and get a solution that uses less logic gates to do the same thing.

 

1: Direct

You check the truth table to see where the output is 1, you get the corresponding function and then you build the circuit.

 

In your example, the output is 1 when (A=0 AND B=0 AND C=1) OR (A=0 AND B=1 AND C=0) OR (the rest...).

 

Basically, X = A.B.C + A.B.C + A.B.C

(Underscores should be overscores)

Then you just draw the circuit.

 

 

2: Optimize

You use Karnaugh Maps.

I googled this site: http://www.maxmon.com/kmaps1.htm

I only scanned through it(i.e. looked at the pictures...), but it seems to provide a reasonable explanation.

 

In your example, you would get something like this:

AB 00 01 11 10

C 0 0 1 0 1

- 1 1 0 0 0

 

(this map is a little crooked, but you get the point...)

 

Then you link the 1's in 2^n groups (1, 2, 4, 8...) and get the corresponding function (check the site).

 

Which in this case is pretty useless, since you get the exact same function.

Karnaugh Maps are very useful in more complicated functions, though.

 

There is a third option left: you do what YT2095 said, and notice that the function is a triple input XOR. But you said you "think it SHOULD be used with AND OR and NOT gates combined", so use the first option.

 

If you want to learn more about this (or if you are forced to, like I was...), you can check this book, which I used last semester to learn this:

Morris Mano e Kime: Logic and Computer Design Fundamentals; Prentice Hall

It's very good, but also expensive. I remember I found the book in a online version a few months ago... google for it.

 

I hope this helped, but I may have said it all wrong. I didn't pay much attention to this stuff last semester.

 

Edit: got the underscores in the wrong place...