A question about truth tables

Question

Hello guys i have a question,
I am trying to make a truth table which consists out of 4 variables
F(A,B,C,D) = B'D + A'D + BD
Is it true on the truth table when for example in B'D we have 0001 or 1001 so B' just needs to be
0 and D = 1 ?
and on A'D A needs to be 0 and d = 1
so the 0111 and 0011 is true for A'D?
I hope i made my point clear thanks!!

Answer 1

How about simplifying first? $$\require{cancel}F(A,B,C,D) = \underbrace{\overline{B}D + BD}_{D\cancelto1{(B+\overline{B})}} + \overline{A}D=\underbrace{D+\overline{A}D}_{D\cancelto1{(\overline{A}+1)}}=D$$

So your truth table will always have $F=1$ when $D=1$, and $F=0$ when $D=0$.

Because I'm bored anyway, here's your truth table: $$\begin{array}{cccc|c} A & B & C & D & F\\ \hline 0 & 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 1 & 1\\ 0 & 0 & 1 & 0 & 0\\ 0 & 0 & 1 & 1 & 1\\ 0 & 1 & 0 & 0 & 0\\ 0 & 1 & 0 & 1 & 1\\ 0 & 1 & 1 & 0 & 0\\ 0 & 1 & 1 & 1 & 1\\ 1 & 0 & 0 & 0 & 0\\ 1 & 0 & 0 & 1 & 1\\ 1 & 0 & 1 & 0 & 0\\ 1 & 0 & 1 & 1 & 1\\ 1 & 1 & 0 & 0 & 0\\ 1 & 1 & 0 & 1 & 1\\ 1 & 1 & 1 & 0 & 0\\ 1 & 1 & 1 & 1 & 1\\ \end{array}$$