In mathematics and mathematical logic, boolean algebra is the branch of algebra in which the values of the variables are the truth values true and false, usually denoted 1 and 0 respectively. Boolean algebra is used in the analysis and simplification of digital (logic) circuits
Questions tagged [boolean-algebra]
463 questions
16
votes
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Why does F + F' = 1?
I have the function: \$f(x,y,z,w) = wx + yz\$
I found its complement function to be: \$f '(x,y,z,w) = w'y' + w'z' + x'y' + x'z'\$
I have to show that: \$f + f '=1\$ but I can't see how to do it.
It seems as if there just isn't anything that…
Carl
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3
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Intuition behind two laws of Boolean Algebra
All along I've learned that the Boolean Operator '.' works like AND and '+' works like OR. This pretty much explains most of the laws of Boolean Algebra; they make sense to me. However I don't quite understand the proof of Absorptive Law…
Ambica Govind
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3
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1 answer
Simplifying a Boolean expression that has 3 variables in it
Problem:
Simplify the following expression using Boolean Algebra:
$$ z = (B + \overline C)(\overline B + C) + \overline{ \overline A + B + \overline C} $$
Answer:
\begin{align*}
z &= (B + \overline C)(\overline B + C) + A \overline{B} C \\
z &=…
Bob
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2
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1 answer
Full-subtractor boolean expression minimization
I'm looking at the standard full subtractor circuit and have been trying to understand how the circuit is derived/synthesized based on a web tutorial.
I can follow the derivation of the truth table in the image below:
Which subsequently leads to…
Dried Apple
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2
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Confusion in Duality Principle in Boolean Algebra
Maybe I have got some misconception while solving a problem.
Lets a logic function,
X=AB+A'C
By applying duality principle, I can say that, X=(A+B)(A'+C)
But I can't prove both are equal. I simplify upto this,
(A+B)(A'+C)=AC+A'B
For an input, A=0,…
Swapnil MZS
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2
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What heuristics are there (if any) to know how close a circuit is to a function?
I'm working on an AI project for circuit minimization.
I'm trying to think of a heuristic to tell me how close a certain circuit is to representing a certain function.
For example, if I need to implement a XOR function, than a circuit consisting of…
Tylor Durden
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2
votes
1 answer
De Morgan minimization
De Morgan
$$y=\overline{a+\overline{b(\overline{c+d})}}+\bar{b}$$
$$y=\bar{a}(\overline{\overline{b(\overline{c+d})}})+\bar{b}$$
$$y=\bar{a}(b(\overline{c+d}))+\bar{b}$$
$$y=\bar{a}(b\overline{cd})+\bar{b}$$
$$y=\bar{a}b\overline{cd}+\bar{b}$$
This…
Ciao
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Are these the same term? Intuition tells me they are the same, but can we derive them one from other?
D+GI vs D+D'GI, are they the sam term ? I even draw a true table for it.
But how can we do it with boolean algebra? Adding a truth table.
Where D+GI is the POS from the table and D+D'GI is the SOP from the table.
I believe they should be the same.
mmmmmmmmmmmmm
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How to prove the SOP and POS are equivalent to one another in XOR Funtion?
Write two Boolean expressions for the Exclusive-OR function, one written in SOP form and the other written in POS form. Simplify both expressions using Boolean algebra reduction and show that the two expressions are equivalent to one another. Draw…
hide on bush
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How to prove boolean algebra rules without truth table?
In boolean algebra I found the rules like the redundancy theorem and de morgan's law, a little unintuitive.
Although the truth table shows it all, I wonder if the rules were made by experimenting like this in the first place, and if not, how do I…
Mahmoud Salah
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1 answer
Digital Logic Boolean Algebra
I am having a hard time understanding why A'+B' is not equal to the following expression:
I understand that when I apply the 4 different combinations: 00,01,10,11 to A and B I get different results for reach expression when we have either the…
CircAnalyzer
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How do I express a Boolean function with don't cares (X) inputs?
I know how to minimize a Boolean function with X as outputs (using K-map).
I have encountered an exercise in which I am asked to write the Normal Disjunctive Canonical Form (NDCF)/ Sum of Products (SoP) but i have X as inputs.
Does it mean I will…
Mr.Hondo
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Implement a circuit for (a+b+c)x+(a+b+c)'x' using only OR and XNOR gates
I know XNOR is AB + A'B' so I thought the equation somehow expands to ax+bx+cx+a'x'+b'x'+c'x', but that doesn't seem right because (a+b+c)' is not the same as (a'+b'+c').
Karan Bijani
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Evaluate \$(\overline ABC\oplus A\overline B) + (\overline AB)\$
I'm struggling with evaluating this one:
\$(\overline ABC\oplus A\overline B) + (\overline AB)\$
I've got to
\$A\oplus B + A\overline B \overline C +\overline ABC\$
But how do I prove that \$A\overline B \overline C +\overline ABC = 0\$
Edit:…
Ilan Aizelman WS
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Identifying a SSOP (standard sum of products) expression
Say you're asked to identify a standard sum of products (SSOP) expression from 4 or 5 options...
3 of them are definitely not SSOP (variables are missing between the terms)... however two of the options are...
None of the above.
AB'.
Solution: It…
The Audience
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