Question

[AND-OR circuit problem]

To my knowledge, NOTed logic gates have little circles at the immediate right of their otherwise non-NOTed versions however, the rightmost gate in Fig. 4-28 has two little circles on its left. What does this mean?

Also, the problem says to use five 2-input NAND gates but, the rightmost gate doesn't seem to be a NAND gate.

Could someone please explain what's going on with this problem?

Any input would be greatly appreciated!

Problem/Solution/Fig. 4-28:
http://postimage.org/image/rl1govyah/

Fig. 4-11a:
http://postimage.org/image/n1tth45sp/

Answer 1

list the inputs and outputs in a table

Answer 2

truth table

Answer 3

Here it is.:
http://i.imgur.com/HBFme0j.jpg

Answer 4

do you think that truth table can help you with your problem?

Answer 5

The circles on the left side of the right-most gate indicate that it's inputs should be inverted. The original circuit had and gates there. SInce you have to use nand gates (they're easier to implement), you'll need to replace the and gate with a nand and invert the output signal of that gate.

Now, as for the right-most gate, it actually is a nand gate in disguise: an or port with inverted inputs. According to De Morgan's laws: \[ \overline{a} + \overline{b} = \overline{ a \cdot b}\]

Answer 6

I see. I didn't know you could just put little circles like that for inverting inputs. Does that change the name "OR gate" to something else?

The question says to use five NAND gates, though so, is the problem badly worded or is the answer not following the instructions of the question correctly? I ask because even though that rightmost gate behaves like a NAND gate, it isn't one. Or am I missing something subtle?

Answer 7

The or gate is just an or gate with inverted inputs. No special name there (for as far as I know).

The or with inverted inputs behaves exactly like a nand gate, so why not replace the two inverters and the or gate with a single nand gate?

Answer 8

"The or gate is just an or gate with inverted inputs. No special name there (for as far as I know)."
Thanks for telling me.

"The or with inverted inputs behaves exactly like a nand gate, so why not replace the two inverters and the or gate with a single nand gate?"
That's what I'm saying! The book says to use five NAND gates and uses four along with an OR gate with inverted inputs. While it does end up being equivalent, (to be pedantic,) it's NOT exactly what the question asked, right? (I just want to confirm that I'm not missing anything important.)

Answer 9

slotema, I don't know if you didn't answer because you're busy or if you thought the conversation was over but, if it's because you thought the conversation was over, could you please confirm or deny what I said?

Answer 10

Sorry for the late reply. I agree with you that it's very sloppy that the solution does not use five nand-gates. It can be confusing and if a question asks for five nand gates, the answer should use five nand gates and not an equivalent circuit.

But the most important part of the question is how to get to a nand-circuit from a boolean function.

Answer 11

It's alright. :) I just wanted to make sure that the reason you weren't answering was because you were busy rather than thinking the conversation was over.

Also, I wanted to make sure especially since I've encountered two problems, so far, with the same flaw of saying "use five NAND gates" but using four along with one equivalent, OR gate (with NOTed inputs).

Anyways, thanks for confirming that it's a flaw in the book and not with my thought process. :)