Questions tagged [boolean-algebra]

In mathematics and mathematical logic, boolean algebra is the branch of algebra in which the values of the variables are the truth values true and false, usually denoted 1 and 0 respectively. Boolean algebra is used in the analysis and simplification of digital (logic) circuits

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How to complete the truth table for a JK flip flop? And why?

I saw this question, but am unsure how to solve it. I have tried various approaches and get some of the answers correct, but never all of them...so my method is obviously wrong For example, what ...
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Convert boolean expression to nand gate only. X = A'B'C+AB'C'+A'B'

I have already made a diagram. However, it won't match the truth table that I have made, which I got from the logic converter in multisim. Could you please help me out with where did I go wrong? Is it ...
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How do you go from gate level to transistor level?

Is there a good method to go from circuit at gate level or truth table to transistor level, other than trial and error? I have an example here to illustate what I am asking. We have the function \$X=(...
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What is the maximum number of inputs to a logic gate that is being used in computing hardware these days?

I was referring to this question, but I had a confusion due to the concept of programmable logic devices. Image from UW page 7. Here the OR section can have up to 8 inputs to it. I'm confused about ...
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Confusion understanding a half adder implementation using 74153 MUX [closed]

As shown here, I have also highlighted the confusing part in the attached snapshot. In the last line of truth table, I know that sum is equal to XOR of two inputs, but here in the last line of the ...
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Design a three input 3bit multiplexer. (Use only NAND gates) [closed]

I need to design a three-input three bit multiplexer but only NAND gates must be used for the same.
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If two Boolean functions \$f_1\$ and \$f_2\$ have same truth table, does that means they have exactly same characteristic? can one f1 numerate to f2?

if \$f_1(x,y,z)=\neg xz+x\neg y+\neg xy\neg z+xy\neg z\$ determine if \$f_1\$ is symmetric and whether it is unate. What I thought is: \$f_1\$=¬xz+x¬y+y¬z, the truth table of \$f_1\$ has the same ...
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5 Variable K-Map with Don't Cares

I stumbled upon this question and I tried doing it but my solution seemed very complicated and I wasn't sure if I grouped everything correctly or, if I did and wrote the correct expression, how to ...
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Line follower robot using only NAND gates

I'm stuck on this and would appreciate some pointers. So for class I have to figure out the logic for a line follower robot using at maximum 8 NAND gates (two 74HC00 Quad NAND ICs). The robot has ...
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I know how to do it with K Maps but how to solve it without using them

Let X=X1X0 and Y=Y1Y0 be unsigned 2-bit numbers. The output function F = 1 if X is equal to or less than Y and F = 0 otherwise. Find the minimized expression for F?
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How to write out a boolean equation with 3 variables and two variables per minterm in sigma notation

I would like to know how to represent a boolean equation with three variables and each minterm containing only two variables such as: Y=AB+A'C+BC into sigma ...
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Creating only NAND/NOT circuit from POS expression [closed]

I created Product Of Sum (POS) expression using a Karnaugh map, and now i have to create its circuit using only NAND and NOT gates. At the start, I created this circuit based on OR and AND gates: ...
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Are the following boolean expressions correct according to De Morgan's laws?

Are the below boolean expressions correct according to De Morgan's laws? I am trying to realise a three input NOR gate using a four input NOR gate, but I suspect I did a wrong transform. \$\:\:\:y=\...
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Pull output down if either of multiple pins are pulled down

(Sorry in case I used the wrong terminology, let me explain.) Context I have a relay board I'm controlling. It has 8 relays, and 8 low level triggering pins for control. 7 of the relays I want to ...
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Boolean function of digital comparator

The boolean equation or function for a binary digital comparator is (A3&~B3)|| (x3&A2&~B2)|| (x3&x2&A1&~B1)|| (x3&x2&x1&A0&~B0). This equation is considered to ...
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My Professor and I are debating about absorption law

So the question is \$(w+y)(wz+wz')wy+y\$ and this is my answer by absorption law where \$A+AB=A\$: $$ (w+y)(wz+wz!)w y + y\\ B A + A $$ So the answer is \$A=y\$. My professor said I ...
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How do you make a three two-input and gates function as four-input and gate

I'm having a hard time trying to recreate this logic. I used the output of my two and gates connected to another AND gate will that work? or is there any better solution to this problem?
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What is the invisible layer between Boolean algebra and the physical circuit of a computer, and how to understand it?

How is Boolean algebra implemented through a circuit ? Is it just a way of thinking about a circuit? You don't need Boolean algebra to think about a circuit since it is made of physical components, ...
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Minimizing delay of Full Adder

It is said that by exploiting the inverting property we can "reduce one inverter delay in each full adder". Why is that? Clearly, we can reduce one for the input of the first adder, but we ...
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Unsure whether or not the following logic circuits I have created are correct

I have recently began studying logic gates and boolean expressions and have been told to label the 2 following logic circuits, as well as derive the full boolean expression for them. I have come up ...
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How do you make a three input NOR Gate function as two input NOR Gate?

Hi this is my first question! So I'm clearly a beginner in electronics and studied for months, now the topic I've studying is logic gates and boolean algebra also the TTL ic. I've been curious if how ...
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What are these letters (not X's) in the boolean inputs in this datasheet?

I'm trying to code the 4-bit initialization process this LCD (page 25) and I'm seeing two rows of bits, with the second containing letters I have not seen before (N, F, D, C, B, I/D, and S). What do I ...
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Number of Prime Implicants VS Essential Prime implicants with don't care

So the Prime implicants are those largest square or rectangle made up of bunch of adjacent minterms Essential Prime implicants are those prime implicants which also cover a particular midterm/s. But I ...
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What boolean algebra simplication is this when applying Shannon's expression

Found this questions about Shannon's expression. While I am trying to follow its logic, found one Super convenience simplification used. Can we do this in general while dealing with boolean algebra? ...
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When do we apply Shannon’s Expansion or what is the motivation using Shannon’s Expansion?

Just confused when following an explanation of Shannon’s Expansion. What does it mean when it says applying Shannon's expression to a? My current understanding is that we replace the variable a with 0 ...
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Can we do this in boolean algebra? Drop same terms first, then apply rules?

Given (W+X+Z)(W'X'+Y)(Y+Z), and would like to prove that it is the same as (W+X+Z)((W'X')+Y). As we can see that the first term,(W+X+Z), is the same, so we can drop it first(correct?) ...
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can we do this, (AB+1)=1 or (A+B+C+1)=1 with boolean algebra?

For example, we have (a + c’d’)(a’ + bc’d’) (bc’d’ + c’d’), can we simplify it to ...
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1 answer
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Are these the same term? Intuition tells me they are the same, but can we derive them one from other?

D+GI vs D+D'GI, are they the sam term ? I even draw a true table for it. But how can we do it with boolean algebra? Adding a truth table. Where D+GI is the POS from the table and D+D'GI is the SOP ...
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I am trying to implement a function using only NAND gates

I am trying to implement a function using only NAND gates. I know I can simply use but my book never mentions such a thing like above. This is a question from my book and I don't understand how I ...
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Why does boolean algebra in electronics use different notation, and are there advantages to this? [closed]

Pretty much only AND makes sense. I can see how it would be more concise to represent AND as "multiplication" when you can potentially have a bunch of variables compared to having to place ...
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Boolean algebra leading leading to an output greater than one?

To my understanding, logic gates take two inputs and give out one input. Consider the or gate below: Since the output is \$A + B\$ suppose that \$A=1\$ and \$B=1\$ (i.e: both wires have current ...
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A boolean algebra question ( K-Map & MPS)

I need to solve this question into a K-Map or a truth table. But I would prefer a K-Map. As we know for Product of sums, the terms inside each bracket must be sums of function which in this case is, ...
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4 answers
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Are there logic gates by which a signal could propagate backwards?

Is there a type of logic gate with floating inputs (I'm using that term loosely) such that a fixed voltage on an output could "propagate backwards?" Let me clarify with examples... Say you ...
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I've tried to make a JK flip flop, but can't get any of the outputs to ever change from 0

I've tried 3 different versions - 1 using AND and NOR gates, another using NAND and another where the the NOR output loops back to the previous gate on the same row (i.e. the top NOR's output goes ...
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3 answers
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Reading the Boolean Expression for a Logic NAND Gate

From https://www.electronics-tutorials.ws/logic/logic_5.html I learned that Boolean Expression for a 3-input Logic NAND Gate is , and is read as "A AND B AND C gives NOT Q". I am wondering ...
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Is the the output of Q' in an S-R Latch used for anything, or is only the Q output important?

From looking at a diagram like this: and watching some videos on the topic, it seems that Q represents a 1-bit memory, but I'm unsure if there is a purpose for Q'.
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4 votes
2 answers
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Get approximate upper bound of 12 bit numbers

I have 8 12 bit unsigned numbers. I want to compute an approximate upper bound(b such that all numbers are less than this number) of these numbers with minimum ...
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How does one go about evaluating complex logic functions (logic gates circuits)? [closed]

I'm tasked with filling out a truth table (in the form of KM) of quite complex circuit and I'm not aware of any reasonably efficient method to do so - other than manually evaluating every possible ...
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Simplifying a Boolean expression with four variables

Below is a problem I attempted from one of the popular books on Computer Architecture. After nearly two pages of work, I am not close to the answer. I am thinking there should be a much easier way. ...
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boolean confirm result

I have solve an exercise and I would like to know if I find the result right. Is there a way so I can check that my solution is right? I think this method is called De Morgan. I had this and I find ...
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Trying to simplify a Boolean expression to \$X + Y + Z\$

Problem: Prove the following Boolean equation using algebraic manipulations: $$ Y + \overline X Z + X \overline Y = X + Y + Z $$ Answer: $$LHS = Y + \overline X Z + X \overline Y$$ \begin{align*} LHS &...
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How do you algorithmically calculate the booth recoding truth table for different radix?

Basically what I am trying to figure out is how one generates algorithmically the truth table for Booth's recoding for different radices of his algorithm. How would you generalize this into a truth ...
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Simplyifying a Boolean Expression that has three variables in it

The following problem can be found at the following URL: Some problems related to digital logic It is problem number 26 on the webpage. Problem: Simplify the following expression using Boolean Algebra:...
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Boolean algebra -- minterms for 1:1 inputs and outputs

Let's say we have a truth table with two inputs (A, B) and one output (X). ...
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Meaning of logic operation " a' "

I have found the following expression: c = (a'.b) what does it mean? I know a.b is a and b (...
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Why do we always implement the complementary of the boolean expression when we design a CMOS circuit?

I am new to implementing boolean expressions in CMOS form, and I understand that the "C" in CMOS stands for "Complementary", so it is an inverter circuit. What I don't understand ...
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Combining MUX 4x1 to represent 5 variable function

I have the following function x’y’zw’v’ + x’yz’w’v’ + x’yzw’v’ + xy’z’w’v’ + xy’zw’v I should implement it using only 4x1 MUX (more than one allowed, of course). I'm clueless on how could I combine ...
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How to convert a Boolean expression from POS form to SOP form?

POS equation is given as F=pi(3,8,12). By converting POS to SOP form directly I get F=sigma(0,1,2,4,5,6,7,9,10,11,13,14,15) But according to the process given in the above picture F is given as F=...
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When do we use minterm over maxterm in real words example or vice versa?

This may sound stupid. We have minterms. It is a product of all variables in a function and that function has the property that it is equal to 1 on exactly one row of the truth table. What do we call ...
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I need help finding out how to prevent my components from exploding (TinkerCad)

Basically, I'm making a logic circuit on TinkerCad and I need to turn on a seven-segment display but some of my components explode and I've got no idea how to solve this. The components I'm using are:...
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