-1

I usually try not ask for homework help but once again I am stuck. I've been going over and over my textbook but I am not able to figure this out. Emailed the instructor and all the help i get is "Check this page" and "check that page", so instead of just not doing it, I would like some advice so I am actually able to learn.

The "G" gate thing, is whats bugging me in the book there is no gate that looks like that so i have no idea what to do. Here's a picture of the question, basically I have to find the X values (outputs). The answer would be nice. But I highly would appreciate a little explaination of "why". Really appreciate the help! Homework

YourFriend
  • 410
  • 1
  • 5
  • 13

2 Answers2

0

Ok, so you you're not quite sure what this G gate means from looking at the diagram. In a question like this (where there's something that doesn't make sense to you), it's helpful to start with what you do know.

From looking at the diagram I don't know what the G gate means. In fact I don't know anything about circuits (but I do know something about logic :) ). I start with the truth table that the author has generously given me the formulas for each gate. I notice that there are 3 operators (*,+,') which I know.

If you know what those operators mean, then you can derive the meaning of the G gate.

Sam Williams
  • 1
0

D looks like an AND

E looks like NAND, the nipple-ish thing is an inverter

F looks like NOT, a buffer with an inverter on the output

G looks like a NOR, an OR with inverted output

The unlabeled one looks like an OR.

That's a really bad drawing though.

Giving you the answer would only cheat you out of your education and this stuff is important. There are 16 logical connectives for binary functions and they're all . . . logical. They make sense.

AND means when both inputs are true the output will be true. "If A and B = 1 output is 1"

OR means if any of the inputs are true the output will be true. "if A or B = 1 output is 1"

NOT means if the input is true the output is false.

XOR means if either input is true, but not both, the output will be true. "If A or B = 1 output is 1 unless both A and B = 1"

AND, OR, and XOR can all have inverters on their outputs which reverses their meanings. When they're supposed to output true they'll output false and when they're supposed to output false they'll output true.

The headings in the table are using * to mean AND, + to mean OR, and ' to mean "invert the symbol on the left".

D is A AND B, so if A and B are true, then put a 1 in the column, the rest of the column is false.

E is B NAND C, so if B and C are true, then put a 0 in the column, the rest of the column is true.

F is NOT C, so put the opposite of C in the column.

G is NOT((A AND B) OR (NOT C)), or if you look at the schematic and think about the formulas a bit you'll see that it's NOT(D OR F). You should be able to figure this out on your own now.

X is G OR E, There's a more complicated formula for it that traces through the circuit like the formula for G, but if you need it to prove your work you'll have to talk to your teacher. You'll probably get more help asking questions that show you put in effort.

I wrote an article about Logical functions in JavaScript that includes schematics. If you memorize the function tables at the top of the article it'll help you a lot when dealing with digital logic. Bonus points for associating the function number with the function name, you'll have memorized the output column of the functions truth table. They've taught you to count in binary right? Anyway, here's the article: http://matthewkastor.blogspot.com/2013/10/logical-functions-in-javascript.html It's not so important for your immediate question but will definitely do you good to read it. Oh, inputs can be inverted as well so don't let that throw you off.

Kastor
  • 617
  • 5
  • 14