Tag Archives: Digital logic

Minecraft Logic

So apparently, creating digital logic circuits on the game Minecraft redstone is a thing.

I was recently sent some screen-captures of the answer to Exercise 34, problem 4. You can create the circuit in the game, and it will give you the outputs for the various inputs. It appears to use an SPST switch for the inputs.

Anyone else out there use the Minecraft game for their Digital Logic studies?

Digital Logic Q & A

Mr. Nance,

I have an overload of questions on digital logic. Hope that is okay!

1. Truth-functional completeness often makes circuits more complicated than they have to be. Is there anything besides cost-effectiveness that is beneficial about truth-functional completeness?

I assume you are asking “Why do we learn how to use NOR gates or NAND gates exclusively in a circuit?” Primarily, it is just to teach students how the gates work. But in practice, if you are constructing an electronic device, you may not have all the gates available (e.g. Radio Shack ran out and will not get them in for ten days), and so need to use a couple of NAND gates to do the job of one AND gate. Also, you might only use one NOR gate in the circuit, but a chip might contain four NOR gates, so why not just use three of them to replace an AND gate instead of buying one?

2. Since the symbol for NOR is the upside-down triangle, is there a symbol for NAND?

The triangle symbol is largely my own convention. See the Wikipedia page for the standard ways of expressing NOR. I know of no special symbol for NAND.

3. Is there a conditional gate (P ⊃ Q)?

Not that I am aware of. You can make a conditional using other gates.

4. Why do we write the names of logic gates in all caps? ( AND instead of and or And)

Just to distinguish them from the words in a sentence. It would be confusing to read “Take an or gate and an and gate…”

5. Why in K-maps do we circle in groups in powers of two?

Because that’s how they work to correctly simplify propositions. Draw yourself a K-map with 0111 across the top four cells, and 1110 across the bottom four cells. If you made two circles with groups of three across and ask, “What variable stays the same (negated or unnegated)?” the answer is that nothing stays the same, so no proposition can be identified. To get the simplest proposition, you must circle the middle four square, and the two on the top right and bottom left. Spend some time thinking through exactly what the K-map is doing when you circle groups and determine the proposition from the circled group. (See the next question.)

6. Finally, do K-maps eliminate the need for the Algebraic identities? I found that doing the Digital Logic Project didn’t require using them.

Yes, that is their primary benefit. Consider the proposition (p • q) ∨ (p • ~q). This simplifies this way:

  1. (p • q) ∨ (p • ~q)  Given
  2. p • (q ∨ ~q)  Distribution
  3. p • 1  Tautology
  4. p  Alg. identity

Now do a 2×2 K-map for this proposition:

 

 

 

See how it does the same thing in a faster, easier way?

Blessings!

Logic with James B Nance

What will I learn in Intermediate Logic?

intermediate-logic-complete-program-dvd-course[1]Logic gives us standards and methods by which valid reasoning can be distinguished from invalid reasoning. It teaches students to think in a straight line, and to justify each step of their thought. Intermediate Logic does this using a symbolic language to represent the reasoning inherent in the language of argument. It is more flexible than syllogistic logic, and can thus apply to more real-life arguments.

Intermediate Logic Unit One teaches the powerful method of truth tables to determine the validity of propositional arguments. Unit Two takes these methods and teaches students how to deduce a conclusion from a set of premises, so they are able not only to show that an argument is valid, but also prove why it is valid. Unit Three teaches these same concepts using the modern method of truth trees. Unit Four applies these methods to the analysis of real-life arguments from 1 Corinthians 15, Hebrews 2, Boethius’ The Consolation of Philosophy,  Augustine’s City of God, and more (including a scene from the movie “Get Smart”). Unit Five teaches the fascinating application of these methods to the logic of digital electronics.

Logic with James B Nance

Audit Intermediate Logic

Would you like to be a fly on the wall in my logic class? Want to improve your understanding and/or teaching of logic by watching me teach and interact with my students, discussing the lesson after the class, and having the recorded class sessions available? If so, click HERE to audit Intermediate Logic for the 2017 school year!

What’s included for Auditors? First, you have access to all the live classes. During the discussion, you will not be called upon as I do with my regular students. You are free to watch in the background by muting your mic and camera, but you also have the option of appearing to ask a question or make a comment if you’d like.

After the regular class time has ended, students leave the virtual classroom while auditors are invited to stick around for a few minutes to ask “Teacher Questions”! This is when you would have me all to yourselves as teachers. Turn on your webcams and mics, and discuss the lesson, teaching logic in general, or whatever questions you might have.

We will meet together live for online recitations Monday/Thursday from 8:00-9:30 AM (PST), or Tuesday/Friday from 8:00-9:30 AM (PST). The spring semester starts January 5/6, 2017, and goes to May 18/19, with a Winter Break in mid-February and an Easter Break in mid-April.

I hope to see you there!