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 .

3083 questions
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Rewrite the function using only NOR

$F=AC'+BC'+BD'$ I know that $AC' -> (A \lnot\lor A) [ (C \lnot\lor C) \lnot\lor ( C \lnot\lor C)]$ ,and $BC' -> (B \lnot\lor B) [ (C \lnot\lor C) \lnot\lor ( C \lnot\lor C)]$ , $BD' -> (B \lnot\lor B) [ (D \lnot\lor D) \lnot\lor ( D \lnot\lor…
Noodle
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Simplify sop expression using Boolean algebra

how can I simplify this sop expression using Boolean algebra ? : $A'BC'D'+A'BC'D+A'BCD'+A'BCD+AB'C'D+AB'CD'+ABC'D'+ABC'D$ I have to use Boolean algebra rules only (no K map); the answer should be this: $A'B+BC'+AC'D+AB'CD'.$ Thanks!
Abdalrahman Abouzaied
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Unable to simplify this Boolean algebra equation $\overline{(AB ⊕ CD) + (D ⊕ A)(\overline{\overline A\ \overline B\ \overline C}})$

Our professor gave us this equation to simplify and after 3 hours and countless attempts I'm still stuck. I'm very new to Boolean logic so thats probably not a good indication at its difficulty :p. Inputs: A, B, C, D Output: Y Anyways here is the…
Flaming_Dorito
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How to simplify the boolean function to get the outcome?

There are two equivalent boolean functions: $$f_{1}(x,y,z)=\overline{z}\wedge(\overline{x}\vee x\wedge\overline{y}\wedge\overline{z})$$ and $$f_{2}(x,y,z)=(\overline{x}\wedge\overline{z})\vee(\overline{y}\wedge\overline{z})$$ The problem is that I…
alekscooper
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How minimize this boolean equation?

I want to minimize boolean equation, but I have no idea how to do. Here is the equation Y = ABC~D + A~(BCD) + ~(A+B+C+D). Can it be minimized?
Aiden
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Boolean Identities: the Distributive law

Need an explanation and solution for this... In Boolean Identities, the Distributive law states that: 1. x (or) 1 = ? 2. x (and) 0 = ? How do I distribute this?
happyNinja1998
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De Morgan's Laws and Boolean Simplification

I have a computer science exam soon, and apparently we are supposed to learn De Morgan's Laws as well as Karnaugh Maps for Boolean simplification. However, I can breeze through Karnaugh maps, but I just don't understand what De Morgan's Laws are and…
Barry B Benson
  • 113
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Testing Boolean functions for linearity, affinity, and bent-ness

Is there any algorithm for testing if given Boolean function is linear, affine, or bent? What are these properties anyway? Can you describe them using human language, not mathematical formulas? Thanks for any response, Frank.
Frank
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Boolean Algebra: How does (x * z) + (!x * y) + (z * y) simplify to (x * z) + (!x * y)

How does the equation: (x * z) + (!x * y) + (z * y) simplify to: (x * z) + (!x * y) using boolean algebra? I've been looking at the various theorems for quite awhile, but I can't figure out how this study guide I found online got to that answer.
Evan
  • 113
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Show that $AB+\overline B = A+\overline B$

Simplify $(\overline A+\overline{AB})\oplus B$. Using Demorgan's Law that $A\oplus B = \overline AB+A\overline B$, I got an answer of $AB+\overline B$. This looked as if it was in simplest terms, but it actually wasn't. If $f(A,B)=AB+\overline B$,…
user535032
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Majority function of 11 inputs

Problem: I need to create a circuit for the 11-input majority function using only AND and OR,assuming that each AND and OR can have multiple inputs (one AND/OR can compute the conjunction/disjunction of multiple inputs). This task has two sub-tasks…
alekscooper
  • 952
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converting a function to maxterm boolean algebra

Consider $f=(A+B+C'+D')(B'+C'+D)(A'+C+D')$ . Is there any simple approach for converting $f$ to multiplication of Maxterms or even sum of minterms?
jack.math
  • 131
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Minimized sum of products form?

Simplify the following Boolean expression. Show your work and list which axiom or theorem you used in each step. Your final equation should be in minimized sum-of- products (SOP) form. M = (A + B'C)(A'D + AB + AB’C + AC')B How can this be done? I…
user532825
  • 33
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Is it ok this DNF of a function of Boole?

I have to find out the DNF of $$f(x,y,z)=x\wedge\left(\overline y\vee\overline z\right),$$ being $f$ a function of Boole. $$\begin{array}{ll} f(x,y,z)&=x\wedge \left(\overline y\vee\overline z\right)\\ &=\left(x\wedge\overline…
manooooh
  • 2,269
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simplification of the function (boolean)

$F(A, B, C, D) = (A'+B'+C')(A'+B')(A'+C')$ I am trying to simplify this and first tried doing something like: $(A'1+C)$ since $x'1$ is still $x$. I then did $1+C=1$, resulting in $A'1 = A'$, for that piece. I did the same for $(A'+B')$, however, is…
Kytex
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