# Reading the Boolean Expression for a Logic NAND Gate

I learned that Boolean Expression for a 3-input Logic NAND Gate is

, and is read as "A AND B AND C gives NOT Q".

I am wondering why it's not read as "NOT (A AND B AND C) gives Q" as this seems to me aligns with the Boolean Expression more.

• These two wordings are equivalent. Aug 17 '21 at 20:15
• Look at Polish notation on Wikipedia. I do not mean yours is Polish notation. But, there are many ways people speak for the same matter.
– jay
Aug 17 '21 at 20:26
• Well, we can't have a say on author's matter of choice. Aug 17 '21 at 20:43
• Or MAYBE because -- Suppose you are designing this function in a CMOS logic, Q' makes more sense. Aug 17 '21 at 20:53

Exciting, what a day! That is the most precise statement. I got the answer from the. posted link!

"Read as" => Read the Symbol from the left to the right: [A & B & C] [gives (the container/function with '&' operation)] [NOT (the hollow dot)] [Q] !!

1. "NOT (A AND B AND C) gives Q" can be perceived as "Not (A & B & C) but something else may give Q", and that isn't a binary opinion.
2. Considering the nuance of 1) feels something off, "A AND B AND C gives NOT Q" sounds like "(A & B & C) gives something (and that is) NOT Q". Better!
• Hi! I have trouble understanding what you mean by "[gives (the container/function with '&' operation)]" and "[NOT (the hollow dot)]". Would you mind explaining this? Also, why isn't "Not (A & B & C) but something else may give Q" a binary opinion? This seems binary to me as I interpret it saying that since (A & B & C) doesn't give Q, the opposite of it, NOT(A & B & C) is what gives Q. Any explanations would be appreciated! Aug 19 '21 at 18:38
• @Cheryl, Thanks for accepting my answer. Meantime I am terribly sorry that my answer wasn't good enough. I will try to explain, but cannot promise to be enough. "[gives]" is an action, which is performed by a "function", which does the '&' operations, which is drawn as a "container", which is a shape of box with round on a side. continue..
– jay
Aug 19 '21 at 18:55
• A meant a "binary opinion" by an answer giving either 1 or 0. That is equivalent to " yes or no", but not "doesn't give Q", which can be taken as "may" (uncertain) give "X (don't care)" or /Q. "Don't care" is not considered as a binary answer.
– jay
Aug 19 '21 at 19:02
• The other hand, (I thought too, that I did not explain enough), wonder if "(A & B & C) gives (/Q)" is more acceptable instead of "(A & B & C) gives something (and that is) NOT Q". I wanted describe there is an action of "gives/outputs" and the whole word, "NOT Q", is an objective noun .
– jay
Aug 19 '21 at 19:10

It is usually read as your suggestion. But there's no contradiction, both statements mean the same. Why the authors of the site you're referring to chose their way of expressing it - no idea.

Boolean logic's overbar notation isn't very friendly to text editors. The electronics-tutorials.ws folks seem to struggle a bit with this.

Here at SE, we can deal. The expression, formally, would be:

$$Q = \overline{ABC}$$

Anyway, I used an SE syntax called mathjax to show this fancy overbar stuff, which codes as follows:

$$Q = \overline{ABC}$$


Now, if you were to code this as a C language expression (C being a language that doesn't know anything about overbars) you'd get:

 Q = !(A && B && C);


They're nevertheless the same expression. As there are so many people who use C, you'll see this form often as it's easier to represent with normal text. Verilog borrows from C and uses this form as well. VHDL? Enjoy your verbose typing...

Anyway, all these forms read as "NOT (A AND B AND C) gives Q", as you said.

Now, to say "(A AND B AND C) gives NOT Q" is a bit confusing, but it's still valid, kind of. Nevertheless, C language and Verilog will not allow a unary NOT operator on the left-hand side of an expression.

That is, this format isn't allowed:

  !Q = A && B && C;    // "(A AND B AND C) gives NOT Q" - nope


While this format is a-ok:

   Q = !(A && B && C);  // "NOT (A AND B AND C) gives Q" - ok


Bottom line: your reading as "NOT (A AND B AND C) gives Q" is preferred to the one given on that website.