Boolean algebra Definition and 153 Threads

is this a valid statement \overline{A\overline{B}} = \overline{A}B

Homework Statement R=(A \cdot \overline{B})+(\overline{A} \cdot B) Using Boolean algebra, including the complement relation D\cdot \overline{D}=0, convert R to a form that uses one NAND, one AND and one OR gate (a total of three gates). Homework Equations de Morgan's theorem...

Homework Statement Ok so I'm having trouble simplifying a part of a boolean equation. It needs to be in the form Yt(...) Homework Equations note X' means Not X The part to be simplified is.. Y(NX'Z+NX'+NZ') The Attempt at a Solution Using the rules of simplification, particularly...

Homework Statement Hey there, I'm having trouble simplifying a boolean expression using XOR and XNOR functions. The final goal is to draw a logic circuit for the expression using NAND and XOR gates only.Homework Equations Assuming W' = Not WW' X' Y' Z' + W' X' Y Z + W' X Y' Z + W' X Y Z' + W...

I'm currently taking a course on Boolean algebra. It's officially named "Mathematical Logic", but I really don't see much resemblance between what I'm doing and other courses of mathematical logic that are taught in the US. It has only been a couple of weeks, but to let you have an inkling of...

Homework Statement Show that F=wy'z+x'y'z+w'xy+wx'y+wxy = y'z+yw+yx Homework Equations Boolean Algebra.. The Attempt at a Solution F=y'z(x+x') + yw(x+x') + w'xy => y'z+yw+w'xy => y'z + y(w+w'x) => y'z + y + yw <-----stuck here what do i do? Not sure if this step is...

How do you know if you can can or can not simplify a boolean algebra expression further?

Homework Statement I've been trying to prove the equivalence between the two statements for quite a while now, any ideas? (A+C)(B+C') = BC + AC' Homework Equations The Attempt at a Solution I used the distributive property to simplify the LHS to AB + BC + AC' Unsure what...

I have a rather technical question in boolean algebra to which I was not able to find an answer. What is the order of operations in boolean algebra? Is it first logical NOT, logical AND, logical OR, and finally logical XOR? Correct me if I am wrong. BiP

Hello, Im trying to understand boolean algebra, I have to do the next problem using Boolean algebra and Identities for this one: So far this what I got: A + /A (A+B) = A + B A + /AA + /AB = A+B A + A + /AB = A + B A + A + B = A + B <-- I think A + A = A so .. A + B = A + B <-- I am not sure...

Homework Statement Homework Equations DeMorgan’s Theorems. The Attempt at a Solution I've had a go at it, not sure if I'm heading in the right direction though. Thanks for any help.

Homework Statement Prove the following through boolean algebra x’y’z’ + xy’z + x’yz’ + xyz + xyz’ = x’z’ + yz’ + xz x’y’w + x’yw + x’yzw’ = x’w + x’yz xy’z + x’y’z + xyz The Attempt at a Solution Well i start by using the commutative law on the first one. x’y’z’ + xyz +...

This is related to logic circuits. How do I simplify this boolean algebra(logic) into its simplest expression? h = (abc + abd + acd + bcd)’ My first attempt would be to change it into product-of-sum. h = (abc)'(abd)'(acd)'(bcd)' and then what next?

I have been asked to simplify this Boolean expression: ~A~B~C~D + ~A~B~CD + ~A~BCD + ~AB~C~D + ~AB~CD + ~ABC~D + ~ABCD + A~B~C~D + A~B~CD I have simplified it down to: ~AB + ~A~C + ~AD + ~C~B But I know that the simplification goes further to: ~AB + ~AD + ~C~B I've looked at...

Homework Statement Lets say I have 4 inputs x1 x0 y1 y0 if I have a sum-of-products say: x1x0'y1y0'+x0y1'y0 can I simplify it to x0y1'y0 by pulling out x0y1'y0 giving x0y1'y0(y0'+1) knowing that 1+y0 is 1 and 1*signalz is signalz. Am I right in thinking this, I really don't want to...

Homework Statement Lets say I have 4 inputs x1 x0 y1 y0 if I have a sum-of-products say: x1x0'y1y0'+x0y1'y0 can I simplify it to x0y1'y0 by pulling out x0y1'y0 giving x0y1'y0(y0'+1) knowing that 1+y0 is 1 and 1*signalz is signalz. Am I right in thinking this, I really don't want to...

Suppose that A is an n-digit binary string: a_{0}a_{1}a_{2}...a_{n} where a_{i} is a member of the set \{0,1\} Now define the following sequence of operations: 1) Complement each digit in A to get a binary string A' 2) A'' = A' + 1 (here + is taken to mean binary addition rather than the...

I was trying a while ago to prove associativity of the XOR operator. That led me to the following problem: I am trying to prove \overline{(\overline{A}*B+\overline{B}*A)}*B + \overline{B}*(\overline{A}*B+\overline{B}*A) = B Obviously it can be solved by just creating a truth table...

Homework Statement I not sure if this is the right place for this, so move me if you need. Ok let's say I have the function xyz+xy'z' - can I pull a x out giving x(yz+y'z') and say that yz=a giving x(a+a') which is x(1) or x. If this is true that means a=yz so a'=(yz)'. Can you distribute...

Homework Statement Simplify the following boolean expression: A'C + A'C'D + ABC + ABC'D I have a solution but when I checked against a boolean algebra simplifier online it gave me a different answer... is there a glaring mistake below ? Homework Equations None. The Attempt at...

Given f(x,y,z)=sum(1,2,3,4) draw truth table find product of sum exprsn find max terms find sum of product truth table x y z out 0 0 0 0 (x'+y'+z') 0 0 1 1 x'y'z 0 1 0 1 x'yz' 0 1 1 1 x'yz 1 0 0 1 xy'z' 1 0 1 0 (x+y'+z) 1 1 0 0 (x+y+z') 1 1 1 0 (x+y+z) sop=x'y'z...

I have a question on my homework that asks me to define a boolean algebra on set B where B = {f|f is a subset of integers squared and f is a function} I need to specify the operations, identity elements and show how to identify the complement elements. I have tried, but am really not...

Homework Statement The question is shown in the picture attached. I have also attached my attempt of the circuit using logic gates. The Attempt at a Solution This is my answer: A’.B.C’.D’ + A’.B.C.D + A.B’.C’.D’ + A.B’.C’.D + A.B’.C.D’ + A.B.C.D’ = B.A’(C’.D’+C.D) + A.C.D’ +...

Homework Statement Prove the identity of the following Boolean equation using algebraic manipulation: AD' + A'B + C'D + B'C = (A' + B' + C' + D')(A + B + C + D) Homework Equations DeMorgan's Theorem: (A + B)' = A'B' The Attempt at a Solution I tried simplifying the equation to...

Homework Statement Prove that in a Boolean algebra the cancellation law does not hold; that is, show that, for every x, y, and z in a Boolean algebra, xy = xz does not imply y = z. Homework Equations The 6 postulates of a Boolean Algebra The Attempt at a Solution I am uncertain as...

Homework Statement Factor to obtain a product of sums. (Simplify where possible.) BCD + C'D' + BC'D + CD Homework Equations Distributive: X(Y+Z)=XY+XZ and X+YZ=(X+Y)(X+Z) Simplification: XY+XY'=X and (X+Y)(X+Y')=X...

Consider a Boolean algebra (B,+,.,negation symbol). 0 is the zero element and 1 is the unit element. + has the lowest precedence and negation has the highest. Show that ô.e+ô.ê+o.e=ô+e for all o and e in B. This isn't a logic gate algebra because that'd be easy, so I can't use the values 0s...

I was asked to make the simplest possible circuit to solve this problem: for an entry of 0000 to 1001 (0 to 9), detect the numbers that are divisible by 2 or 3. I decided to write the truth table with an output of 1 for functions that are NOT divisible by either 2 or 3, since that seemed like...

Homework Statement A'B'C' + ABC' + A'BC + A'BC'. The ' denotes a bar over the previous letter. Homework Equations Simplification Rules The Attempt at a Solution C' (A'B' + AB) + A'B(C+C') C' (A'B' + AB) + A'B ... or like so: A'B'C' + ABC' + A'B Is it possible to simplify...

Homework Statement I am suppose to use Boolean algebra to show that the following expressions are true. Homework Equations w'z' + w'xy + wx'z + wxyz = w'z' + xyz + wx'y'z + wyz The Attempt at a Solution I have tried to figure out how to get to that answer above but I am stuck...

Hello all I don't write much, I mainly follow you silently. Great forum I have a doubt that to many of you will seem absolutely silly but it has been bugging me for days. I am trying to find the correct interpretation to a non-english administrative act and trying to use all possible...

Homework Statement Hey PF! I'm supposed to "Optimize the equation for minimal input-output delay with 3-input NAND gates of 1.8ns delay each." It'll become much clearer at my attempt at a solution, I hope. Homework Equations De Morgan's laws, K-maps, the sort... The Attempt at...

We were taught both methods to minimize gates. I frankly just want to pick one method all the time and become an expert in it, rather then try them both. So, according to your experience, which method do I better pick?

Homework Statement There should be lines of some values to imply the "Not" form of them, however to make it easier, i'll just use the ¬ Symbol (a) Let x, y be elements of a Boolean algebra. Prove from the axioms that (x · y) + x = x. (b) Prove from the axioms of Boolean algebra that x...

Hey all So i just need some clarification, though I hope I am posting in right section (this is not a HW Q) I was told to find the simplest Product of Sums(POS) and Sum of Products(SOP) 1st 2nd 3rd...

Homework Statement 1. Simplify the following problem using boolean algebra: (p+q'r')(p'q'+r) 2. Use algebra or karnaugh maps to simplify the following circuit: (z+xy')+yx+xzy'Homework Equations Boolean algebra rules and demorgan's lawThe Attempt at a Solution 1. (p+q'r')(p'q'+r)...

Homework Statement Identify the equivalent binary numbers of the following P term and S terms( which are the subscripts of P's and S's) Ex: P?=AB'CD' Homework Equations No equations that I know of The Attempt at a Solution I create an table to find the subscripts for P and S...

Hello. I am wondering if the distributivity theorem works for factoring out more than a single term. Distributivity Theorem: BC + BD = B(C + D) But can I do this: [ tex ] ABC + ABD = AB(C + D) [ /tex ] Thanks.

Homework Statement Produce the given truth table (given below as well as in a neater version in the attached Excel document) using the Boolean operators AND, OR, and/or NOT: A (Input 1) B (Input 2) O (Output) 1 1 0 1 0 0 0 1 1 0...

Is boolean algebra "hard" compared to calculus or ODE's? What's a rigid boolean algebra? And since I shouldn't start a new thread, can anyone recommend a good boolean algebra book? Thanks for your answers!

Homework Statement Looking at the characteristic equation for a SR flip flop we have Q+ = QR¬ + S It's known (from the associated K-map of the SR/SC flippy floppy) that (Q+)¬ = Q¬S¬ + R K-maps are useful as they do the simplification for use, but I'm trying to use algebra to get from Q+ to...

May seem easy, I can't do it though... I'm given an identity to prove:- (A + C).(notA + B) = A.B + notA.C I've started with LHS, multiplied out and ended up with an extra B.C. I think this has something to do with the distribution rule but I don't know how to work it through Any help...

I have the following function to be reduced/simplified. F(A,B,C,D) = BC + (A + C'D') where ' denotes the complement Here's my solution: = BC + (A + C'D')' = BC + (A + (C+D) = BC + (A + C + D) = BC + C + A + D = C(B + 1) + A + D = C*1 + A + D = C + A + D Is this correct?

Homework Statement http://img525.imageshack.us/i/circuitg.png/ Get boolean equation and apply De Morgan. Homework Equations The Attempt at a Solution I'm not sure how to do this. Treat CLK like an variable? If so, is this correct? F = abC + AbC + ABC I do not know. I suppsoe you then...

Homework Statement is B={0,1,R,F,X) a boolean algebra? Use basic posulates/axioms to prove it. R=Rising F=Falling X=Dont Care Homework Equations Reference: Boolean Identities Table The Attempt at a Solution it is boolean algebra. you can create and, or , not tables with it...

can anyone help me simplify this expression.. f(x,y,z)=(x+y+z')(x+y'+z')(x'+y'+z).. :confused:

x+(y.z) = (x+y).(x+z) I don't understand how one gets the RHS. Could you please it? There must be some reasoning involved. Please help me. Thanks.

Hi I'm not a science or physics student - quite a layman. Therefore, please keep your replies simple and explanatory so that your guidance and help can be fully appreciated. Thanks. What are these logic gates - AND, NOR, NAND, etc? Are these some physical circuits? In Boolean algebra...

hey there.. can someone help me with the problem given.. Problem.. simplify b ⊕ c' Homework Equations The Attempt at a Solution i don't know how to attempt this question.. can someone can give me an idea to start.. thanks in advance

Hi, I'm having some trouble solving one of the problems from my homework assignment. Homework Statement Prove: P((AB)C) = P(A(BC)) Where A,B,C are either true or false. Homework Equations We can't do this by using a truth table, we can use the following equations: P(A + B) = P(A) + P(B) -...