Right so I'm trying to understand truth tables in the context of digital logic. And paticularly with lettered boolean expresssions.
Now I do understand truth tables, you have either true or false as the value, and you have some operators that determine that true or false answer. And, Or, Not etc.
But the set of questions I've bene set, I can't get my head around. It's asking for things like ABC + ~A~B~C. I'm not sure what this expression actually means.
Can anyone explain to me what the questions in the below image are asking me to do? These are the questions i've been set.
I do actually have the answers but I honestly can't figure out why it works like that.
Thank you for your time.
Authentication is required for your links, so most of us cannot actually see what you are talking about, but for this bit:
In boolean algebra, multiplication is "and", addition (+) is "or" and the tilda (~) is negation ("not"). Thus we read "(A and B and C) or (not A and not B and not C)"
This says "Either $A,B,C$ are all true or they are all false." Which is another way of saying "Their boolean values are all the same."
So let's fill out the truth table
$$\begin{array}{c:c:c|c:c|c} A & B & C & A~B~C & \bar A~\bar B~\bar C & A~B~C + \bar A~\bar B~\bar C \\ \hline 0 & 0 & 0 & 0 & 1 & 1 & (0\cdot 0\cdot 0)+(1\cdot 1\cdot 1) = 0+1=1 \\ 0 & 0 & 1 & 0 & 0 & 0 & (0\cdot 0\cdot 1)+(1\cdot 1\cdot 0) = 0+0=0 \\ 0 & 1 & 0 & 0 & 0 & 0 & (0\cdot 1\cdot 0)+(1\cdot 0\cdot 1) = 0+0=0 \\ 0 & 1 & 1 & 0 & 0 & 0 & (0\cdot 1\cdot 1)+(1\cdot 0\cdot 0) = 0+0=0 \\ 1 & 0 & 0 & 0 & 0 & 0 & (1\cdot 0\cdot 0)+(0\cdot 1\cdot 1) = 0+0=0 \\ 1 & 0 & 1 & 0 & 0 & 0 & (1\cdot 0\cdot 1)+(0\cdot 1\cdot 0) = 0+0=0 \\ 1 & 1 & 0 & 0 & 0 & 0 & (1\cdot 1\cdot 0)+(0\cdot 0\cdot 1) = 0+0=0 \\ 1 & 1 & 1 & 1 & 0 & 1 & (1\cdot 1\cdot 1)+(0\cdot 0\cdot 0) = 1+0=1 \end{array}$$