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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consider a base 16 adder how to modify the adder so that it can perform a base 8 addition

Consider a base $16$ adder. How can I modify the adder so that it can perform a base $8$ addition? I expect this question will appear in my exam tomorrow; if anyone can give me a hint or a solution, I'd be grateful. I've tried searching the net and…
user155971
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consider a base-16 adder. explain how to modify the adder so that it can perform a base-10 addition

consider a base-16 adder. explain how to modify the adder so that it can perform a base-10 addition I found this when I searched in Google but not understand please guide me to understand this question so that I can solve it
user155971
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DeMorgan's Law with Boolean Algebra

So I'm studying for an Assembly Language final tomorrow and I'm trying to simplify the following expression using Boolean Algebra. Here are the steps I've written so far, am I safe in assuming that this is a proper process and answer? The answer my…
secondubly
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Trying to simplify boolean algebra a+ac+ab

I am trying to simplify A+AC+AB. I think I have solved it, but I want to double check its right, can it be simplified to A+A(C+b) and then again to A(C+B) as A+A = A?
Lukas
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Simplifying Boolean Function with Karnaugh Map

How to write Product-of-sum(POS) and Sum-of-product(SOP) Above K-Map? I already write POS please check my answer.
user2534252
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Simplifying a Boolean Expression 2

The boolean expression is as follows: (¬A^¬B^¬C)∨(A^¬B^C)∨(A^B^¬C)∨(A^B^C) I have found that A⊕(¬B^¬C) is equal to the above but I have absolutely no idea on how to get this result, I have spent hours simplifying the above expression and time and…
Paul Shirebrook
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How to prove that $abd = abcd + abc'd$ for all general occassions

It is true for example that $abd = abcd + abc'd$. Each of the terms on the right part of the equation contains all the used letters. Is there anyway to prove that any term is equal to the sum of the terms that contain it and and all the used…
Alice1nw0
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Simplifying boolean algebra expression $(AB+AC)'+A'B'C$

$$\eqalign{(AB+AC)'+A'B'C&=\overline{(AB+AC)}+\overline A \,\overline BC\\&=(\overline A+\overline B)(\overline A+\overline C)+\overline A\,\overline BC\\&=\overline A+\overline B\,\overline C+\overline A\,\overline BC\\&=\overline A+\overline…
user2534252
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Boolean algebra - neutral elements

I am searching for the neutral elements of following Boolean expressions: -NOT -NAND -NOR The neutral element of NOR should be 0 (false) but the others? I think for NOT and NAND there are no neutral elements exisiting. Thank your for your help!
queenD
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How to simplify the given boolean expression to simplest form?

I have the expression xy+xy'z+x'yz'. I have tried a number of ways to simplify it. What approach will ensure that this expression is reduced to its simplest form?
277roshan
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Boolean Algebra, using DeMorgan's law

I have obtained this function: $$(\overline{A}*D) + (\overline{A}*C) + (\overline{B}*\overline{D})$$ ... after I have used Karnaugh Map to simplify the canonical expression. And now, I am needing to get and equivalent expression using DeMorgan's law…
Alberto Fernández
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Write the following Boolean expression in product of sums form?

Write the following Boolean expression in product of sums form: a'b + a'c' + abc is it correct if I write it as the following ? (a+b')(a+c)(a'+b'+c')
user155971
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Simplify the Boolean expression $X Y Z+X Y' Z'+X' Y' Z+X' Y Z'$?

$$X Y Z+X Y' Z'+X' Y' Z+X' Y Z'$$ I know it simplify to (X XOR Y XOR Z),BUT I want to simplified using only AND, OR, and NOT Gates? Please help I spent three hours but I don't get the same truth table.
Abdalla
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Boolean Algebra Simplification

I have to simplify A'BC' + A'B'C + A'BC + ABC My result was A'BC Is this correct?
Brandon Jerz
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Boolean algebra simplification a'bc+ab'c+abc'+abc

Can't figure out how to simplify $(^\neg a)bc+a(^\neg b)c+ab(^\neg c)+abc$, I'm really bad at this...
Brandon Jerz
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