I know that $\overline{p + q}$ will result in the input to the logic gate being p, and q, and we can negate this by using an or gate, followed by a not gate, or we can just use a nor gate.
However, In my homework, I also encounter the same question with $(\overline{p + q)}$.
Which leads me to ask this question, does this expression mean something different
(e.g. negate $p$ and $q$ BEFORE passing it to the or gate, or is it exactly the same?)
Furthermore, if one had: $\overline{\overline{A}B}$, is it safe to assume that we would first negate the $A$, and then pass $\overline{A}$ and $B$ in to an and gate, followed by a not gate, or similarly passing $\overline{A}$ and $B$ in to a nand gate?
I know this is an elementary question – I'm just trying to completely understand the syntax as it will allow me to improve my understanding of this topic.
Thanks.
Best Answer
The intent of the author almost surely comes as the same for $\overline{p + q}$ as for $(\overline{p + q)}$. In other words, the author probably means the same thing by both strings. However, syntactically they do differ significantly, in that the second could potentially fit a set of formation rules for a logical system, while the first will not since all expressions with binary operations need parentheses in infix notation.
The answer to your second question is "yes".