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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Simply to minimum literals

F = AB'C + A'BC + ABD + CD' + D' I started by doing D'(C+1) and reducing (C+1) into 1, resulting with D'1 which is just D'. I now have AB'C + A'BC + ABD + D', and cannot seem to find another way to reduce this further, though I know this cannot be…
Kytex
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Boolean Expression simplify

I have this expression: $$(x + y + z’)(x’ + y’ + z)$$ which I am trying to simplify. I decide to multiply it out in order to get, $${\color{red}{(xx')}}+(xy')+(xz)+(yx')+{\color{red}{(yy')}}+(yz)+(z'x')+(z'y')+{\color{red}{(z'z)}}.$$ I know that…
Kytex
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Looking for steps/theorems for this Boolean algebra conversion

I'm usually pretty good at Boolean algebra, but I can't seem to figure out the theorems/steps involved in the following equation conversion: C = AB + AD + BD to C = AB + D(A xor B) Any help is appreciated. Thanks
b.knight
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Truth table boolean algebra

I'm trying to make truth table for this and im terrible in boolean algebra. Can someone help me? (A'+B')C+ABC'+A'C
Mateusz Zablocki
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Manipulation of Axioms for Boolean algebras

The laws of Boolean algebras are given. The identity laws (13): $p \land 1 = p$, $p \lor 0= p$, the complement laws (14): $p \land p' = 0 $, $p \lor p' =1$, the commutative laws (18): $p \land q = q \land p$, $p \lor q = q \lor p$, and the…
Metta World Peace
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Boolean Algebra with decomposition property

Does there exist a (countable) Boolean algebra $(B,\bigcup, \bigcap, 0, 1)$ with the following property: $\forall A\in B\setminus \{0\}$ there exists $A_1,A_2\in B$ such that $A_i\neq A$, $A_1 \bigcup A_2 = A$ and $A_1 \cap A_2=0$. (e.g. in…
Tom Q
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If A + ~A = 1 why ~A*~B*~C*~D + A*B*C*D != 1?

In Boolean algebra the law says that $A$ or complement of $A$ is $1$, then why $ABCD$ or its complement $ABCD$ is not also $1$ ?
Alex
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general strategies for maximizing boolean simplification from a specific example

I'm trying to completely simplify $$F_0 =A' B' C' D' + A' B' C' D + A B' C' D' + A B' C' D + A B' C D$$ I got as far as $$\begin{align} &= A’B’C’ + A B' C' D' + A B' D\\ &= A’B’C + AB’(C’D’+D)\\ &= A’B’C + AB’(C’D’+D)\\ &= A’B’C +…
Joe Stavitsky
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Convert Boolean AND-OR to OR-AND

How can I convert a'b'c + a'bc + ab'c + abc' to an equivalent OR-AND. I cannot seem to find a solution that mirrors the truth table. I've tried the Distributive Law as well as using De Morgans Law without success.
pstatix
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A'C+AB - can it be simplified?

I had a really big expression that i've simplified to:A'C+AB. I just wanted to check with everyone that it can't be simplified any further. There's no trick to factor out the A' and A is there? In general, how do you know whether you've got the…
user513043
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Karnaugh's map single dot

I had to create a DNF from table c. Which results in 'p'q'r + 'p'qr + pq'r. Than I had to create Karnaugh's map from it, resulting in: +----+----+-----+------+-----+ | | QR | 'QR | 'Q'R | Q'R | +----+----+-----+------+-----+ | P | | | …
O'Niel
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Given a truth table, is there a way to know if it's possible to create any/all logic gates?

Is it possible to do without brute forcing it? | a | b | out | --------------- | 0 | 0 | 1 | | 0 | 1 | 0 | | 1 | 0 | 1 | | 1 | 1 | 1 | I managed to bruteforce my way through it and figured that it is possible to implement AND/OR/NOT gates, but…
integralfx
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Is the term 'Sum of min-terms' same as 'Standard SOP form' in Boolean Algebra?

I want to ask that if we are told to express an Boolean Expression in sum of min-terms which is already in non-standard SOP form. So do we need to express it in Standard SOP form or what? For Example: Express the following Boolean Function in sum of…
Khubaib Khawar
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Why doesn't there exist the following Boolean identities?

There are various Boolean identities some of which are as follows: $A + A = A$ $A . A = A$ $A + 1 = 1$ $AB = BA$ $A + AB = A$ and the list goes on But why doesn't there exist the following Boolean identities which to me seems correct ? 1) $A + B…
Ahtisham
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Solving Boolean expressions

Can anybody help me to solve the below expression. A'B'C+A'BC+AB'C+A'BC'+AB'C=AB'+A'B+BC I'm so lost just been trying to get it for awhile only using the 10 boolean simplification rules.
Kanha
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