Mathematics Stack Exchange
Mathematics Stack Exchange

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 .

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Boolean Algebra Simplification POS

I'm given this expression $$ (x+y'+z')(x'+z') $$ the $'$ meaning not. I have to simplify this to 3 literals and show my answer as a product of sums. Every calculator I check says the answer is $(x'y')+z'$. So far all I can think of to do as the…
rileypitcher
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help simplifying this boolean expression

xyz’+x’yz+xyz+x’yz’ I have to simplify this expression and return the results in products of sums form in one literal. If I simplify as sum of products I can get y as the answer or one literal but not sure how to express it in product of sums form
rileypitcher
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Boolean Logic Simplification: (A+B)'(A'+B')'=?

I am trying to simplify the following Boolean expression : (A+B)'(A'+B')'=? but I am really new in boolean algebra, so please can anyone explain to me how to do it.
Eleftheria
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What does $x*$ mean?

I am trying to understand what the operator $*$ means in Boolean algebra. If x is a Boolean variable, what does the expression $x*$ mean?
Bob
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Boolean expression A׳B׳C+A׳BC׳+AB׳C׳+ABC'

How do i simplify this boolean expression with steps? I am so lost for some reason. I entered it into my logic converter on multisim and did recieve the simplified version. A׳B׳C+A׳BC׳+AB׳C׳+ABC'
Elijah W
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Reducing a boolean expression with nested ternary expression

Consider the following boolean expression with a nested ternary expression: $$(\text{if $a < 0$ then $-a$ else $a$}) < 3$$ I can "see" that it can be reduced to: $$a > -3 \land a < 3$$ However, I can't figure out the algebraic rules I need to apply…
Good Night Nerd Pride
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Boolean function equivalent

The following Boolean function equivalent to. F(A,B,C,D) = PI(1,3,5,7,13,15) a)BD' + ACD' b)BD'+ACD+ABC'D c)(B+D')(A+C+D') d)(A+D')(B'+D') I wrote down the truth table for 4 input. I tries simplifying the SOP expression but it is not matching with…
Abhiram M V
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Sum of Products in boolean algebra

What is the minterm equivalent of A' + B'? The options are 1)sigma(0,1) 2)sigma(0,1,2) 3)sigma(1,2) 4)sigma(1,2,3)
Abhiram M V
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Memory and bits. Need some help

Could someone check over my answers to verify I am correct. Say we have a memory consisting of 2048 locations, and each location contains 16 bits. ◦ A) How many bits are required for the address? Answer: 11 bits ◦ B) If we use the PC-relative…
Bdk Fivehunna
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Proof of Demorgan's theorem by Principle of Duality. Is it valid?

I chanced upon a seemingly "too good to be true" proof of Demorgan's theorem for boolean algebra, however I'm not quite sure if it's valid. The principle of duality states that for a boolean algebra, changing all OR signs to AND signs, all 1's to…
buggy
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NOT ((NOT A AND NOT B) OR (A AND NOT B)) simplification using de morgans law

I had my AS mock exam today, and this question came up. I've checked it on calculators and it says it simplifies to B, which is what I got in the exam, but I'm not entirely sure how I got there. My understanding is that if you want to change the…
Liam Michel
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Boolean Algebra simplification help

A'B'CD' + A'BCD + AB'C'D + AB'CD + ABC'D' I have tried using a k map and I got it down to AC'D' + A'B'CD' + A'BCD + AB'CD. Also I think AB'C'D + AB'CD can be simplified to ABD' Trying to simplify this. Any help would be great! Thanks
peterlany1975
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Represent the following function $X \rightarrow Y$

Let the functions $\blacktriangle $ and $\blacktriangledown$ be defined as $X\blacktriangle Y = \sim (X\wedge Y) $ and $X\blacktriangledown Y = \sim (X\vee Y)$ Represent the following function ( only use $\blacktriangle $ and…
Daniel Andersson
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a) Show De Morgan's law $\sim (X\blacktriangle Y) \leftrightarrow (\sim X\blacktriangledown \sim Y)$

Let the functions $\blacktriangle $ and $\blacktriangledown$ be defined as $X\blacktriangle Y = \sim (X\wedge Y) $ and $X\blacktriangledown Y = \sim (X\vee Y)$ a) Show De Morgan's law $\sim (X\blacktriangle Y) \leftrightarrow (\sim…
Daniel Andersson
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if $B$ is a boolean algebra and $a\neq b$ in $B$ there exist an ultrafilter containing $a$ but not $b$.

Suppose $a$ and $b$ are distinct elements in a boolean algebra $B$. I am trying to show there is an ultrafilter on $B$ containing $a$ but not $b$. Does this follow from the fact (is this a fact?) that $a = \wedge \{F:F \text{ is an ultrafilter on B…
Dman
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