Question

Boolean algebra question:
Does A'C'D' + A'C'D' stay as it is or does it merge into a single term?
In other words, is the identity x + x = x applicable here?

Answer 1

x+x is 2x
What is the meaning of A'C'D'?

Answer 2

A' = not A.
Boolean algebra.

Answer 3

http://www.cs.science.cmu.ac.th/person/chumphol/204231/Basic%20Identities%20of%20Boolean%20Algebra.jpg

Answer 4

what value is x,y,z
are those suppose to be 1's and 0's

Answer 5

x = 1
x' = 0

Answer 6

Well since you do have x+x
you can use the identity 5 there

Answer 7

\[A'C'D'+A'C'D'=A'C'D'\]
\[x+x=x\]

Answer 8

x'y'z' =/= (xyz)' thought

Answer 9

-t*

Answer 10

x'y'z' = (x+y+z)'

Answer 11

if it was (ACD)' + (ACD)' i wouldn't even be suspicious and write (ACD)' straight away

Answer 12

\[(A+C+D)'=A'C'D' \text{ assuming we can expand that the thingy using 15 } \\ \text{ but \in the \end this will still give us the same thing } \text{ \because }\\ (A+C+D)'+(A+C+D)'=(A+C+D)'= A'C'D'\]

Answer 13

but I kinda want to do some reasearch into this notation
i'm not too faimilar with it
and i'm assuming things I don't know anything about yet
like i assume (A+C+D)'=A'C'D'
I don't even know if (x+y)'=x'y' can be expanded to three variables

Answer 14

oh is + sign just the bit wise operation exclusive or?

Answer 15

Yes it can be done even on whole expressions, it's called DeMorgan's law if you want to look it up.

Answer 16

+ Is basically OR

Answer 17

now the only thing I need to know what is the meaning of xy

Answer 18

like is that and?

Answer 19

xy means x and y right

Answer 20

Yes there's a "multiplication" between them, aka AND

Answer 21

so just for fun...
A C D A' C' D' A' and C' and D' (A' and C' and D') or (A' and C' and D')
T T T F F F F F
T T F F F T F F
T F F F T T F F
T F T F T F F F
F F T T T F F F
F T F T F T F F
F T T T F F F F
F F F T T T T T
As you see we have shown
A'C'D'+A'C'D'
=A'C'D' by truth table
your initial thingy about applying x+x=x was correct

Answer 22

Oh right! I know I was missing something, completely forgot about the truth table and k-map.

Answer 23

Man thanks for responding I was really desperate with that one.

Answer 24

np
I was just not used to the notation
I was like omg what does this all mean

Answer 25

That's some determination I must admit, diving in like that in a new subject.

Answer 26

Just proved it's just A'C'D' using k-map as well.

Answer 27

well no I was just used to different notation