# Addition, multiplication, and apostrophe used to represent boolean algebra expressions?

I'm looking at a worksheet that expresses boolean logic expressions using multiplication, addition, and apostrophes; something I've never seen before.

I can make a guess that the apostrophe is equivalent to ¬ (except it's suffixed instead of prefixed). But I'm not sure what the addition and multiplication of the variables/propositional atoms would mean. Furthermore, I don't know how a boolean logic formula can "output" something other than just a truth value...

I can't seem to piece together with certainty the meaning of this representation. Could anyone take a look at the below example and maybe make a guess as to a translation of this representation to the more traditional ^, v, and ¬ symbols?

This arose in the context of digital logic in terms of logic gates and such on a CPU, if that makes a difference.

An alleged truth table of the above two expressions (the first row is filled in as an example):

• @ShyPerson Thank you very much! I guessed that but didn't think it worked, but looking back now it would make sense! Do you know why they have a specific term written in the box? Is that just the term in the expression that turns out to be true, do you think? Nov 4, 2019 at 12:52
• @JamesRonald: Yes, it looks like that's the term that makes the whole expression true. Nov 4, 2019 at 19:16
• @YuvalFilmus: Thanks for the encouragement to create an answer. I guess I'm still unsure about when to create a comment versus an answer. Is there some documentation somewhere that would clarify this? Many thanks Nov 4, 2019 at 19:17
• @ShyPerson Generally speaking, it’s better for questions to have an answer. Nov 4, 2019 at 19:18
• Do not post pictures of formulas, please. You can use LaTeX to type them, it's a lot more polite and generally friendlier. Nov 4, 2019 at 19:25

Usually $$+$$ means $$\lor$$, "multiplication" means $$\land$$, and $$'$$ means $$\lnot$$.