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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 .

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Simplifying three variables boolean algebra

$$F(A,B,C)= (AC+ABC')(BC+B'C')= A(C+BC')(BC+B'C')$$ What is the next step? Please help me I'm stuck
Chika
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K-Map resulting in a simplified function of 1

I hope the title wasn't butchered but I'll do my best to explain here. I am trying to find the simplified function of $F$ using a K-map and after going through everything I arrived at the simplified function of $F=1$ which doesn't seem right so I…
AFC
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Are these two boolean expressions equal?

I am working on some homework and I was wondering if I was able to do the following, I will show you all of the work I have done so far for the context, I am working on getting the complement of F. $$ F=(a+c)(a+b')(a'+b+c')$$ $$…
AFC
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Prove that $\neg 0 = 1$ in every boolean algebra.

I am trying to prove that $\neg 0 = 1$ in every boolean algebra by using the laws of boolean algebra. The assistant told us to start by using the identity law and form $\neg 0 = 1$ to $\neg 0 = \neg 0 \cdot 1$. However I don't know how to proceed…
user376765
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Proving or disproving a basic equation in Boolean algebra

I need to prove or disprove that in any Boolean algebra: if $a+ab=b$ then $a=b=1$ or $a=b=0$. I build the following truth table: $$ \begin{array}{|c|c|c|} \hline a & b & a+ab \\ \hline 0 & 0 & 0 \\ \hline 0 & 1 & 0 \\ \hline 1 & 0 & 1 \\ \hline 1 &…
vesii
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Simplifying the expression using Boolean Algebra Part 2

Simplifying the expression using Boolean Algebra into sum-of-products (SOP) expressions . refers to AND + refers to OR Updated with new question ( (a + b) ∙ (a' + c') )' + (b + c')' + a∙b'∙c = ( (a + b) ∙ (a' + c') )' + (b' . c) + a∙b'∙c = (( a ∙…
Lawrence Wong
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Boolean algebra - subtraction and inverse doubt

How to simultaneously solve these boolean expressions? A' + AB = 0 AB = AC AB + AC' + CD = C'D     where ' means conjugate. So this might seem silly but: a) I have never heard of subtraction in Boolean. b) I have never heard of inverse (NOTE: Not to…
PLAP_
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Boolean Algebra Simplification of $(A + B + C') \cdot(A'\cdot B' + C)$

Good Afternoon all, I am having trouble simplifying the expression $(A + B + C') \cdot(A'\cdot B' + C)$, I've tried converting $A'\cdot B'+ C$ to $( A' + B' + C)$ and factoring it with the other term but I don't think this is right. Could anyone…
T S
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Simplifying Boolean Expression with Multiple Parameters

Can someone help me simplify tis boolean expression, I have been trying all morning with no luck. It has multiple parameters and I have no idea if I have to use De Morgan and when. The expression is: ABC + DE + AF +ABDF + A'F All i come up with is…
se rebbi
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Returning 1 if both bits are are not zero

I'm trying to create a function where 0x04060002 and 0x00080008 would return 0x000X000X because each of the other positions have at least one zero. Any nonzero number can go where the "X" is. I've tried &-ing and |-ing but I can't seem to find…
tsent123
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Product of Sums to Sum of Products

I apologize if this is a dumb question, but I'm having some trouble seeing how we can go from the Boolean equation P = (P1 + P2)(P3 + P4)(P1 + P3)(P5 + P6)(P2 + P5)(P4 + P6) to P = P1*P4*P5 + P1*P3*P5*P6 + P2*P3*P4*P5 + P2*P3*P5*P6 + …
John Roberts
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Understanding Duality in Boolean Algebra

The dual of every true statement is true. Though this is simple, I am having difficulties understanding this. For example, $A + A = A$ and $A . A = A$ are dual; and indeed they are both true. But let us take the statement $A = 1$. Obviously, this…
Truth-seek
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Question on the free BA on countably many generators

Let $A$ be the free Boolean algebra of countably many generators. As a Boolean algebra, it is isomorphic to the field $F$ of clopen subsets of its Stone space, namely, the Cantor space $X=2^\omega$. It is known that $A$ is atomless, countably…
Beginner
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How to show these two expressions are equivalent using Boolean Algebra?

I have two boolean functions: $$f(a, b, c, d) = \bar{a}cd + a\bar{c}d + ab\bar{d} + abc$$ and $$g(a, b, c, d) = d(a \oplus c) + ab$$ I know these two functions are equivalent because I tried every combination by using a truth table. Now, can…
Truth-seek
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simplification of F=A'B'C'+A'B'C+ABC'

enter image description here have i grouped them right? is the answer A'B'+C' or not???
Rafael
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