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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Proving relation in boolean algebra, need help

Here is the logic equation and I am trying to prove the relation ($'$ stands for complement): $$_1_3' + _2'_3' +_1_3 +_2'_3 = _1'_2' + _1_2 + _1_2'$$ What I am doing: $$x_2' (x_1x_3' + x_1x_3 + x_3' + x_3)$$ $$x_2'(x_1(x_3' + x_3) + x_3' +…
UserMoon
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How can I prove that (x and ¬y) or (¬x and y) = ¬((x and y) or (¬x and ¬y))?

I'm stuck at this problem: (x and ¬y) or (¬x and y) = ¬((x and y) or (¬x and ¬y)) Basically what I have to do is to convert the right side of the equation to the left side using boolean algebra. I tried using De Morgan and other theorems, but I can…
xxsl
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Boolean algebra-dual of an expression

Can anyone think of an expression that is equal to its dual ? I've been trying to solve this for the past 2 hours, but nothing comes to mind.
markus
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simplify boolean expression: xy + xy'z + x'yz'

As stated in the title, I'm trying to simplify the following expression: $xy + xy'z + x'yz'$ I've only gotten as far as step 3: $xy + xy'z + x'yz'$ $=x(y+y’z) + x’(yz’)$ $=x(y+y’z)+x(y’+z)$ But I don't know where to go from this step, I'm not sure…
secondubly
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Karnaugh map minimal representation

Find the minimal representation for: $f(w,x,y,z)$ = summation $m(0,5,6,8,13.14)+d(4,9,11,12)$ I was a little confused what to do with the don't cares but I used all of them. Based on the Karnaugh map I made $4$ groups: $w'y'z'+y'z+wx'+yz'$ Then to…
Lil
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Boolean algebra simplification

Is this the simplest form of the expression? Given: $$x'y'z+x'yz'+x'yz$$ My work: $$x'y(z'+z)+x'yz'= x'y+x'yz= x'y(z)$$
Lil
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XOR of two numbers AND third number ?

If: x & (a ^ b) != 0 Then one of the following holds: x & a == 0; x & b != 0 or x & b == 0; x & a != 0 What is the reason for this? And are there similar properties of AND/OR/NOT with XOR? Thank you.
simplename
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Boolean algebra proof (a+b) (a+c)' = a'bc'

I have to prove that (a+b) (a+c)' = a'bc' My algebra skills are really rusty and I was wondering what identities are used to solve this so I can get a better understanding
Brandon Jerz
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Equivalence of the two boolean expression

This is a question from a textbook on digital logic which I am having a difficult time with: Prove that the following expression is…
Nen
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Boolean algebra: Minimizing a product of sums expression?

For the life of me, I can't figure out how to get this into minimal product of sums form. Any help is appreciated. (a+b+c)(a+b'+c)(a+b'+c')(a'+b'+c')
Mike9060
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How to directly translate a boolean function to a boolean formula which expressed by conjunctive normal form?

How to interpret the conjunctive normal form to a practical meaning?
zty
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Where am I going wrong with this Boolean simplification problem?

I am self-studying the Nand2Tetris course. I am trying to simplify the Or logic gate as much as possible to simplify my HDL-specified circuit. Using the Sum of Products, I write the following for the Or truth table: (~A.B) + (A.~B) + (A.B) = (~A.B)…
intelli78
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Prove $(A\wedge B)\vee(A\wedge-B\wedge C)\vee(B\wedge-C)=(A\wedge C)\vee(B\wedge-C)$

Let A, B and C be digital inputs. Prove that the following boolean equation holds true for any given values for inputs. (A AND B) OR (A AND (NOT B) AND C) OR (B AND (NOT C)) = (A AND C) OR (B AND (NOT C)) This is a question with no solution in my…
user1075375
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Simplifying a function using POS and boolean algaebra

I have a function, $$ f = (A+B\cdot \overline C) $$ I am trying to simplify it this form using the inverse function $\overline f$ from the truth table (by anding the rows which form a '0' result). $$ \overline f = (\overline A + \overline B +…
Prasanth Ravi
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Boolean algebra: $(x+y)(x’+z)(y+z) = (x+y)(x’+z)$

Could someone explain to me how this simplification is derived? $(x+y)(x’+z)(y+z) = (x+y)(x’+z)$
Alec
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