Tagged Questions
3
votes
1answer
34 views
Boolean Algebra Transform
I am revisiting Boolean algebra after a long while.
Can somebody help show me how to simplify the LHS to get the RHS?
$$abc * a'bc + (abc)' * (a'bc)'\quad = \quad \;b'+c'$$
1
vote
2answers
57 views
Prove that $(S \cap T = \varnothing) \land (S \cup T = T) \rightarrow S = \varnothing$.
Logically, the following proposition makes sense:
$(S \cap T = \varnothing) \land (S \cup T = T) \rightarrow S = \varnothing$
Or, in english, if sets $S$ and $T$ share no elements, and the union of ...
2
votes
2answers
70 views
How to prove that $(A \lor B) \land (\lnot A \lor B) = B$
I know this is fairly basic, and I understand that it becomes
$$
\begin{align}
(A \land \lnot A) \lor B \\
F \lor B \\
B
\end{align}
$$
However, I can't work out how to prove that it becomes that ...
3
votes
1answer
41 views
How do I find the size of this set?
For homework, I need to show that the size of a certain set is $\le 2^{(3n)^k}$ but I'm not getting this (I think I may just misunderstand how the set is defined).
So the set is defined as follows:
...
2
votes
2answers
26 views
Get A⊕(B+1) from A⊕B
I have numbers A,B,C.D.
(⊕ is XOR)
C = A⊕B
D = A⊕(B+1)
Is there any way to get D from C, when I do not know A and B? How?
Thanks for help!
2
votes
2answers
59 views
Proving if Boolean Equations are valid
I need to prove algebraically that:
$$ab + abc'd + abde' + abc'e + a'b = b$$
$$(wxyz)(wxyz' + wx'yz + w'xyz + wxy'z) = 0$$
3
votes
3answers
412 views
De-Morgan's theorem for 3 variables?
The most relative that I found on Google for de morgan's 3 variable was: (ABC)' = A' + B' + C'.
I didn't find the answer for my question, therefore I'll ask here:
...
1
vote
1answer
76 views
Reduce following expression to one literal, boolean algebra
$$W'X(Z'+Y'Z)+X(W+W'YZ)$$
The goal is to reduce the following to one literal
So after I expanded it out, i got the following:
$$W'XZ'+W'XY'Z+WX+W'XYZ$$
Now from here, I got stuck and didn't know ...
2
votes
3answers
48 views
How can I prove this logical expression?
I've already confirmed that the following expression is true with a truth table, but I need to prove this with other Boolean expressions for my assignment. The $\oplus$ symbol is exclusive or in this ...
0
votes
2answers
112 views
Simplifying Boolean Algebra
I am trying to prove that BC + !A!B + !A!C = ABC +!A
I have attempted using De Morgan laws, and substituting X for !A!B and ...
-4
votes
1answer
174 views
Boolean Algebra (Help Needed)
How would I draw the gate-level logic circuit of the following Boolean expression?
$$
(((A \land B \lor C) \lor D \land E \land F) \lor G \land (H \lor I \land J)).
$$
Then how would I implement this ...
0
votes
2answers
43 views
Conjunctive normal form of logical expression
I tried to convert this to a CNF-expression but failed.
What did I do wrong? Or are there simply missing steps?
$$ F' = (( A \lor \lnot B) \land C) \to ( \lnot A \land C) $$
Removed Implication
$$ ...
2
votes
1answer
316 views
Boolean Algebra - Product of Sums
I converted from a truth table to sum of products and simplified that easily. What I am having problems with is simplifying the product of sums for that same truth table. I have:
NOTE: $A' = ...
2
votes
2answers
104 views
Logic gates analyses
How to write the output of the gates not, and, or, xor, nand and nor in terms
of their inputs, expressed as zeros and ones, using base 10 addition and
multiplication.
Thanks much in advance!!!
2
votes
2answers
344 views
Simplifying the following expression using Boolean Algebra
Simplify the following expression using Boolean Algebra into sum-of-products (SOP) expressions
. refers to AND
+ refers to OR
a'.b'.c' + a.b'.c' + a.b.c'
This is what I have so far.
a'.b'.c' + ...
