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Questions tagged [boolean-algebra]

Boolean algebras are structures which behave similar to a power set with complement, intersection and union. Use this tag for questions about Boolean algebras as structures, or about functions defined from/to Boolean algebras. For Boolean logic use the tag propositional-calculus.

Boolean algebras are structures which behave similar to a power set with complement, intersection and union. Use this tag for questions about Boolean algebras as structures, or about functions defined from/to Boolean algebras.

A Boolean algebra uses Boolean variables, typically denoted by capital letters, e.g. $A,B$, which can only take the values $0$ or $1$. Operators are $\land$ (conjunction), $\lor$ (disjunction) and $\lnot$ (negation).

For Boolean logic use the tag .

3083 questions
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Which is the simplest boolean expression of ab + (a + b)' + (a'b)'?

I have this Boolean expression: $y = ab + (a + b)' + (a'b)'$ $ = ab + a'b' + a + b'$ $ = a(1 + b) + b'(1 + a')$ $ = a + b'$ Is $(a + b')$ the simplest answer or: $a + b' = (a'b)'$ the simplest? Thank you for help.
Viet Nguyen
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How does this boolean expression simplify?

I was able to simplify a boolean expression $$(\neg a*\neg b*c)+(a*\neg b*\neg c)+(a*b*\neg c)+(a*b*c)$$into the form $$\neg b*(a\oplus c)+a*b$$ where $*$ is the logical and, $+$ is the logical or, and $\oplus$ is the logical XOR. Apparently, from…
user281997
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why is (b *c)+(a*c) = c?

I have been learning boolean algebra but I am stuck understanding a rule. That is the term I am trying to explain my problem on: $$(\neg a*\neg b* \neg c)+(\neg a*\neg b * c)+(\neg a *b *c)+(a*\neg b*c)+(a*b*c)$$ I first cut it down to this: $(\neg…
Zesa Rex
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How is the distribution law working in this Boolean Algebraic equation?

I am working on a sample boolean algebraic question as study for my upcoming exam, my full expression is $(A\overline B(C + BD) + \overline{AB})C$ I have simplified my expression to $A\overline BC + \overline {AB}C$ My example papers solution book…
Ninja2k
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How does $(xy' + x'y)'$ simplify to $(xy + x'y')$

How does $$(xy' + x'y)'$$ simplify to $$(xy + x'y')$$
Redjman
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boolean algebra XOR parity

Let $f, g$ be two functions from $x_1, x_2 , ..., x_n$ to $\{0,1\}$. Prove that the function $h$, defined by $h = (f\text{ XOR }g)$, maintains the following attribute: $N(h) = N(f) + N(g) - 2*k$, when $N$ is defined to be a function which operates…
Jonathan
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How to prove that $b \wedge 0 = 0$ in a boolean algebra?

It seems a rather obvious fact, but how can we prove that $b \wedge 0 = 0$ for an arbitrary element $b$ in a boolean algebra. Where $0 := c \wedge - c$ for any element $c$ of the boolean algebra, and the axioms for complement are $(b \wedge -b) \vee…
MathsCS42
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Why does $ I \wedge a = a$ hold true?

In boolean algebra the following is true (From Wolfram): $ \emptyset \wedge a = \emptyset $ $ \emptyset \vee a = a $ $ I \wedge a = a $ $ I \vee a = I $ Where $I$ = the universal set Why are 3 and 4 true? If $I = \{0,1\}^n$ and $a=\{0,1\}^n$…
BanksySan
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Inverter circuit (From new "operation")

If I have this truth table how can I make inverter circuit such that F(x)=~x x y x⊡y 0 0 1 0 1 0 1 0 0 1 1 1 Example of other circuit: I really don't have an idea. Thanks
Math Newbie
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Simplify boolean expression X'YZ + XY'Z + XYZ'

i have this expression to put in the XOR forms. X'YZ + XY'Z + XYZ' The steps i did already are these ones: Z(X'Y + XY') + XYZ' Z(X^Y) + XYZ' But if i put the same expression on WolframAlpha it says that the final solution should be: XY ^ XZ ^ YZ ^…
MatPag
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Convert my truth table into boolean exp

I have this truth table: CD | 00 | 01 | 11 | 10 AB | | | | ------+----+----+----+---- 00 | 1 | 1 | 0 | 0 ------+----+----+----+---- 01 | 0 | 1 | 1 | 0 ------+----+----+----+---- 11 | 0 | 1 | 1 | …
Cholesky
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Boolean on Hexadecimal

I need help with ANDing two hex values but my approach is not working. Question - Evaluate the following Expression 0x77 && 0x12 My Attempt I was told that you can divide up each hex digit into 4 blocks. This worked for bigger values such as 77 but…
Ninja2k
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simplify the function, and implement them with two-level NAND gate circuits

$$(A'+C'+D')(A'+C')(C'+D')$$ how to simplify it. i got $A'D'C'$, but it's probably wrong. can someone help me
samexmm
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boolean algebra: simplify 3-term dnf form covering a|~a

Its been a while since I've dealt with boolean algebra, so I'm trying to simplify the following equation using wikipedia:Boolean_algebra:Laws while double checking everything in sympy: ~[(a & b) | (~a & c)] Applying De Morgan's twice leads to CNF…
user19087
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Basic Discrete Math Logical Proposition

If -1 - 1 = 0 then tomorrow is Thursday. Why is the answer True? -1 - 1 does not equal 0. I seem to be struggling with this concept, and I can't seem to word my question correctly to get a good google explanation for an example like this.
X33
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