Boolean algebra Definition and 146 Threads

EDIT: My apologies if I started this thread in the wrong forum! Homework Statement Z = P.Q.R + P.R Where . = AND + = OR ~ = NOTHomework Equations (Commutative Law) A+B = B+A, A.B = B.A (Associate Law) (A+B)+C = A+(B+C), (A.B).C = A.(B.C) (Distributive Law) A(B+C) = AB+AC...

Homework Statement [PLAIN]http://img340.imageshack.us/img340/7690/123rk.gif Homework Equations The answer should be A'C' + A'D'The Attempt at a Solution Shown in above in the question. I want to know how can i get the correct answer. As you see above, in my last step, I wonder whether B'+BD...

http://img710.imageshack.us/img710/2314/booleanalgebra.jpg AFAIK logic is all about "T"/"F" or 0/1, and boolean algebra is all about logical manipulation. But there seems to be something wrong since there is a boolean algebra with more that 2 objects in it`s set. So, can I have some...

1. Prove that for all boolean algebras if x+y=x+z and x'+y = x'+z then y=z. 2. Homework Equations : x+x' = 1, xx'=0, basically we are allowed to use the usual boolean algebra properties. 3.Attempt: This the second part of a problem, in the first part we had to give and example of...

1. Homework Statement and attempted solutions Simply each of the following Boolean expressions: i) http://img69.imageshack.us/img69/4438/equa1.jpg ii) http://img69.imageshack.us/img69/9907/equa2.jpg iii)Expand the following SOP form to proper miniterms (don't forget to delete...

Homework Statement Prove (x+y)(y+z)(x'+z) = (x+y)(x'+z) Homework Equations The Attempt at a Solution On LHS, i have done till =(y+xz)(x'+z) 1st- distributive =x'y+yz+xz 2nd- distributive(2ce) =(x+y)(x'+z) 3rd-? For third procedure, what properties should be...

Homework Statement My book contains this boolean algebra theorem: A + notA * B = A + B I have verified the validity of this statement using truth tables, but I find that I am unable to derive it. Our professor gave us a few steps to simplify Boolean expressions: 1) change all...

Homework Statement F(x,y,z)=X'Y'Z + X'YZ+ XY'Z + XYZ' + XYZ The Attempt at a Solution F(x,y,z) = X'Y'Z + X'YZ+ XY'Z + XY (Z'+Z) F(x,y,z) = X'Y'Z + X'YZ+ XY'Z + XY I am stuck here l don't know how to further simplify it so that l can end up with F= XY + Z

Okay, so I'm stuck at a step of a much bigger problem where I have to simplify a boolean function. Homework Statement Here is where I'm stuck, I have to change the left hand side to the right hand side. How do I prove this with the rules of boolean algebra? CA + CB + B'A = CB + B'A...

Guys I need your help! :cry: I've never liked boolean algebra, with conjugation, disjunction, implication, equivalence and all that stuff because I considered very easy to understand. But what I can not understand is implication (I get headaches from implications :frown:) Here is what I do...

Homework Statement Find the minimum Sum-Of-Product Expression for: f = ab'c' + abd + ab'cd' The Attempt at a Solution By introducing the missing variable in term 1 and term 2 I can get an expression that has all the variables: a, b, c, and d. I do so by: f = ab'c'd + ab'c'd' + abcd + abc'd...

Ok, I am having a difficult time with the following problem. I am to show that the two sides are equal. x1'x3 + x1x2x3' +x1'x2+x1x2' = x2'x3+x1x3'+x2x3'+x1'x2x3 For the LHS I can simplify it to: x2(x1'+x1x3') + x1'x3 + x1x2' x2x1' + x2x3' + x1'x3 + x1x2' x1'x3 + x2x3' + x1x2' For the...

Hi guys, I'm new to boolean algebra, i couldn't get this through... a'b'c' + abc = 1 ? or i have to use (abc)' + abc = 1 to get 1 ? Thanks you.

Digital Logic is blowing my head off! I can't understand a thing. I had a question in which I was supposed to simplify the function F= A'+B'+(A+B).B'.C apperently this simplify to 1. Here's what I managed to do: F= A'+B'+[(A.B')+(B.B')].C by Distribution F= A'+B'+(A.B').C by Tautology F=...

I need to simplify these boolean expressions. Homework Statement Problem A: a`b`d+a`bd`+bc`d`+bcd`+ab`c`d+b`cd Problem B: a`b`cd+a`bd+abcd+a`b`d+acd+abd+ab`c`d Problem C: a`b`c`d`+a`b`cd`+a`bd+ab`c`d`+bd+ab`d`Homework Equations abc means a AND b AND c a+b means a OR b a` means NOT a The...

Homework Statement Hi, I am trying to write the sum and output of a full adder in terms of XOR logical functions using boolean logic and Karnaugh maps. I've got the expressions from the Karnaugh maps fine but I can't seem to rearrange them into the expected form shown at the end of my...

Homework Statement An irrigation system should open sprinkler's water valve when if the system is enabled and neither raining nor freezing temperatures are detected. Homework Equations S\rightarrow system enabled R'\rightarrow not raining F'\rightarrow freezing temperatures not detected...

[b]1. (A+B+C')(A'+B'+C)=A (XOR) B + (A XOR C)' + (B XOR C)' Expand right hand side first and then show tht its equal to left hand side by using truth table. I am unable to expand the right hand side i need help thnx

What is the difference between a boolean algebra and a complete lattice? What are their similarities?

I was wondering how you can prove using Boolean algebra, x + x'.y = x + y I know we must manipulate either side of the equation but I'm just not sure how I can. Can anyone offer me some help.

Homework Statement AB + (A' + B')C + AB Homework Equations I've simplified many problems, but this one is giving me trouble. I know the answer is AB + C, but for some mental reason, I can't seem to come to that answer. The Attempt at a Solution STEP 1: AB + A'C + B'C + AB...

Hi Everybody, I have a general question: Is there any Algorithm that can do Boolean Algebric Reduction ? Appreciate your help

Hi, This is a question about a boolean "law" type behavior I've noticed in my homework a couple of times. Basically i can't find a boolean algebra law that permits this optimization short of using a k-map. So I'm just wondering if theirs some way to optimize the one equation using...

what exactly is it? i have a friend that has to take it, he's an audio engineering major at UMiami. i forgot to ask him when i saw him last

show that x'yc+xy'c+xy = yc + xc + xy The Attempt at a Solution - my first attempt at the solution was this: c(x'y+xy')+xc >>> c(y+x)+xc >>> yc+xc+xy I can't remember if that is valid or not. I seem to remember that A'B=B, but not sure. Can somebody please help me?

Homework Statement Simplify these equations and functions 1. xyz’ + x’ (x + z) + x’yz + x’y’z’ 2. xy (z + z’) + x’y’z 3. wxyz + w’xy’z + wx (y’ + z) + w’x’z 4. F(A, B, C, D, E) = ∑(0, 1, 5, 6, 13, 15, 20, 21, 22) 5. F(w, x, y, z) = ∑(0, 1, 2, 3, 11, 13, 15) Homework Equations...

According to my notes, the definition of an embedding from a boolean algebra B in a boolean algebra B' is an injective map f:B-->B' such that for all x,y in B, f(sup{x,y}) = sup'{f(x),f(y)} and f(Cx)=C'(f(x)), where sup is the supremum in B and sup' is the complement in B', and where C is the...

[b]1. Simplify the following equations using boolean algebra [b]2. a) abc + ab'c'+ ab'c b) (abc)'+(a+c)'+b'c' [b]3. Please help me to solve the above equations

Simplify the following expressions using Boolean algebra. a. AB + A(CD + CD’) b. (BC’ + A’D) (AB’ + CD’)

Homework Statement Sketch a CMOS logic circuit that realizes the function Y = AB + A'B'. This is called the equivalence or coincidence function. Homework Equations The Attempt at a Solution The top is connected to Vcc... Is this correct? I'm learning this on my own and...

Homework Statement 1) Simplify the following Boolean expression: Y = ABCD – ABD Homework Equations The Attempt at a Solution I simplified it in the following way: Y = ABCD – ABD. (C + 1) = - ABD But the answer given in my book is ABD.

I was doing a problem, and the distributive problem hit my head, as I kind of blanked out on this one. Can B'D' + BD be simplified into a smaller equation? Because I'm thinking it's impossible to do so. (You may be able to apply Demorgan's theorem, but that doesn't really simplify the...

Boolean Algebra, Logic Diagram, K-Map, Nor gates... HELP! Homework Statement F(A,B,C,D) = Sigma(2,4,6,10,12) d(A,B,C,D) = Sigma(0,8,9,13) [Dont Care Functions] Implement the function using no more than 2 NOR gates. Homework Equations K-map The Attempt at a Solution First of all, I...

I just started Digital Systems coursework and it seems our professor felt like giving us a book that has no examples and progresses the class with no examples as well. So basically we are stuck trying to learn Boolean algebra reduction with no real guidence. Great. Anyways, I'm looking...

For my digital logic class, we are supposed to prove all of the two and three variable properties (commutative, associative, distributive...). I'm not really sure how to go about this, because although he didn't say, it seems intuitive to prove them in order, ie you can't use a property until...

Here's the problem: a'b'c'd' + a'b'cd' + a'b'cd + ab'c'd' + abc'd' I've gotten it down to: ac'd' + b'c'd' + a'b'c Having trouble coming up with a way to simplify it more...Is this as far as it can go? Any help appreciated, thanks...

I would like you guys to check over my Boolean Algebra equations to see if I did them right. My teacher uses the same symbols as the computer science books Legend: http://img218.imageshack.us/img218/2948/xnor5qv.jpg [/URL][/URL][/URL][/URL][/URL]=[/URL] XOR XOR =...

Hello everyone, I'm designing a IC that will result in a 1 output if the number is > 9. So I wrote out the truth table and or'ed all the min terms and got the following: http://img282.imageshack.us/img282/482/lastscan45vd.jpg I'm stuck now! any help would be great!

Boolean algebra problem! Hello everyone 'im designing a IC that will tell output a 1 if the number is > 9. so I wrote this boolean expression but I'm stuck on reducing it. B' = B compelemnted AB'CD' + AB'CD + ABC'D' + ABC'D + ABCD' + ABCD AB'(CD' + CD) + AB(C'D' + C'D + CD' + CD) any...

Hello everyone I'm having problems proving this: note: A' will stand for complemented; AB + BC'D' + A'BC + C'D = B + C'D B(A+C'D') B(A+C'+D') BA + BC' + BD' + A'BC + C'D BA + BD' + A'BC + C'(B+D) B(A + D' + A'C) + C'(B+D) now I'm stuck, i don't see how that is going to work out. Any...

Boolean Algebra Hard! hey all, got stuck on some boolean algebra just wondering if you all can check my working out thanks :) basically the ` represent bar's and in the example no. 1 the p is barred, r is barred,and the overall function is barred hope you get the gist of things thanks 1...

hey all, got stuck on some boolean algebra just wondering if you all can check my working out thanks :) basically the ` represent bar's and in the example no. 1 the p is barred, r is barred,and the overall function is barred hope you get the gist of things thanks 1. [(p` + qr)(pq+r`)]` my...

I was just wondering if anyone could lend me some guidence in the boolean equation AB(A+B)= X when the last "B" in the formula has a bar above it.. thanks

If anyone knows anything about the basics of Boolean Algebra please tell me what you know. Thanks ----- Life is a problem... SOLVE IT!

An example in the book asks us to implement the XOR (exclusive-or) function using only 2-input NAND gates. So: f = x_1 \overline{x_2} + \overline{x_1}x_2 If we let \uparrow represent the NAND function. That means that: f = (x_1 \uparrow \overline{x_2}) \uparrow (\overline{x_1} \uparrow...

I think I am missing part of my notes, or at least I don't understand them: if x+y = y+z and xy = xz, then x=z x = (y+z)x Absorbtion (Don't really know where this is coming from) x(y+z) Commutative xy+xz Distributive It stops here and starts again at: yz+xz (I have...