how to create an electronic circuit

Welcome to AAC!

Since the parts you have selected are surface mount, you will either have to make a PCB, or find an adapter (they are available).

Just curious, why are you stuck on these parts? They are hard to use, and one you solder them in will not be very reusable.

A through hole set of components and a protoboard are 100% reusable. The book links shown above have some good experiments on the subject.

DIGITAL INTEGRATED CIRCUITS

 

If you wish to reduce your chip count you can do this with a single QUAD 2-INPUT NAND Gate,
one NAND gate and two gates as inverters for B' and Q'. You will have one spare NAND gate.

 

I could have shown you a circuit diagram (which you should draw) but I'm glad that you figured it out on your own.

 

And what you have discovered, more or less, is that any logic circuit can be implemented using only two-input NAND gates (or, it turns out, only two-input NOR gates).

Here's a little exercise to help you explore this. Imagine taking the circuit you started with and changing it so that it was an OR instead of an AND. In other words, what if you had wanted to implement Q= A OR NOT B? Can you figure out how to do that using one a single quad NAND gate package? Hint: You could actually implement two of these circuits that are completely independent. In other words, you only need two two-input NAND gates which makes trying a brute force search of all possible configurations pretty easy.

If you can figure out how to do that, then you have just figured out how to apply what is known as DeMorgan's Theorem. So you might want to read about it in the near future.

While expressing things as

Q = A AND NOT B

is okay in some circumstances, you will want to start getting used to using the more common Boolean algebra notation. In this, AND is represented the same way as normal multiplication, so AB, (A)(B), A(B) and A*B would all be seen as (A AND B). The OR is represented the same way as normal addition, so A+B would be see as (A OR B). The NOT is represented a few ways. The one I like the best is using a trailing apostrophe. So A' is the same as (NOT A). Other methods are to use the asterisk, so A* is NOT A. For this reason, I tend to not use the asterisk at all, because some people look at it as indicating an AND and others as a NOT, so if YOU use it, it is a good practice to include a note indicating what you mean by it. The other common way to show the NOT is with a leading slash, either forward or backward. Hence, A', A*, /A, and \A are all common representations of (NOT A).

One thing to watch out for is that the inversion does not distribute, meaning that AB' is the same as (A AND (NOT B)). If you meant to say NOT (A AND B), then that would be expressed as (AB)'. And, again, the NOT does not distribute, so (AB)' is not the same as A'B'.

Don't worry about getting all of this down right now. Just keep in the back of your mind that when working with logic expressions, you need to be careful and explicit. You'll learn the specific rules as you go forward.

 

btw, there are two ways to create a NOT gate from a NAND gate. You have shown one way. Can you show the other to indicate that you understand?

Then do the same with a 2-input NOR gate.

 

What WBanh is leading up to is something called De Morgan's Theorem (or De Morgan's Laws) or rather, De Morgan's Identities.

Check this out on the web and let us know if you need help.