Questions tagged [karnaugh-map]

A Karnaugh map (or K-Map) is a diagram that assists with simplifying Boolean expressions. The method takes advantage of a human's pattern recognition ability as an alternative to performing potentially complex calculations.

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K-map: how to decide which implicant to be prime

I am a bit confused about deciding which implicants to turn into prime. If I group implicants 1 and 2 into a bigger implicant, can I group implicants 2 and 3 as well? For example, if I have the K-map ...
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How is the boolean expression for mux2 and mux4 deduced?

I've been looking at the following article: https://www.electronics-tutorials.ws/combination/comb_2.html I am confused as to how the boolean expression Q = a'b'A + ab'B + a'bC + abD is deduced for ...
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Finding functions for JK / D / T flip flops

I am trying to understand this concept of flip flops. Given some Karnaugh Map, all I need to know is how to find the functions of various flip-flop types: sr flip-flop (\$s = \text{ ??} \quad r = \...
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Implementing function with NAND only quickest way

I'm trying to remind myself how to implement given function or karnaugh map with NAND or NOR gates. I remember how DeMorgan's laws work. Let's say I have some Karnaugh Map and I want to implement the ...
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What are essential prime implicants in this example?

F(A,B,C,D) = Sum (0,2,3,5,7,8,9,10,11,13,15). The prime implicants are represented in different colours as below and the equation of the function is found to be F = B'D' + BD + CD + AB'. I tried to ...
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Can a circuit that shows an error if a 4-bit number is higher than 9 be simplified to “(DC) + (DB)”?

I need to build a circuit that accepts a 4-bit number and turns on a LED (representing an error) if the given number is higher than 9. As I understood, it should represent an "error display for a BCD ...
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Problem finding SOP form of f + g

I have a project and I am asked to find the sop form of f+g and find its cost and then compare it to the cost if I implement f and g separately. I am trying to find SOP form of f+g and I am stack ...
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Creating coder of MFM linear code (Miller) using logic gates

I have a problem with the implementation of my MFM encoder using logic gates (in the CEDAR program). It's not working correctly, and I don't know if this is software problem, or if I'm doing something ...
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What is the general mathematical proof that K map and Boolean Algebra are equivalent?

Is there a mathematical proof that shows K map always reduces the Boolean expression into it's minimal form?
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Shorthand SOP/POS conversion

I have Sigma ABC (0,1,2). To convert from sigma to prodocut sign i just should put the numbers which are left. But my question is up to which number i change ? Is it 2^3=8 ( because i have 3 variables)...
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How to get minimum product of expression in Combinational Circuit Design (PLA)

I've been answering an assignment where the problem is design a combinational circuit design using programmable logic array (PLA) Here's the problem: F1 (A, B, C) = π(0,1,2,4) F2 (A, B, C) = π(1,...
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How to transform a 3 variables Boolean Function into a K-map when some variables are not specified in the expression? [closed]

I looked at the already answered questions and used google, but I didn't found anything that explains the thing clearly. My problem is that I don't know how to solve function like ...
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Karnaugh Maps in POS instead of SOP

From my understanding, to use karnaugh maps to simplify an expression, you would have an SOP expression that does not have to be canonical and then group the 1s in the table. So that got me wondering....
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How to convert following Karnaugh map to a simplified Boolean expression?

This is the Karnaugh map which I draw for F = A'B'C'+AB'C+A'BC+ABC' But I am not sure how to simplify the Boolean expression for this as there are no groups here
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7 Segment Display Segment C Kmap Confusion

I am working on the Kmap for the Segment C on the 7 Segment Display. The list of numbers that light up the 7 segment displays segment C are as follows: The Kmap I came up with, without grouping yet, ...
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K map minimization need confirmation

So I have to solve this f= ∑m(0,4,10,17,21,26,27,31)+ ∑d(1,5,7,8,11,16,19,20,23,24,25) Please tell me if this is correct:
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Converting boolean function (dnf) to only 2-input NANDs

I'm currently preparing for an exam and was doing some exercices regarding boolean logic. Commonly asked question is to build a function from a truth table and simplify it with a karnaugh map. After ...
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Easiest way to get minterms from a SOP Boolean expression?

So far, I've come across problems were I need to get the list of the minterms in a truthtable from a SOP Boolean expression. For example; They way I've tackled these problems was to convert the ...
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Karnaugh Graph Simplification

I have following truth Table : F(w,x,y,z) = Σ(0,2,5,7,8,10,12,13,14); ...
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State Machines - What happens to 'Don't Care's in the Output?

This is referencing the article about state machines on allaboutcircuits.com In their state table, they have a 'Don't Care' listed under the output for the state 11. However, in their k-map of the ...
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522 views

K-maps, do they completely simplify?

I've been told that K-maps produce a completely simplified boolean equation, and they can't or shouldnt be simplified anymore after that. However, on allaboutcircuits.com they were able to simplify an ...
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Karnaugh Map and Mirroring

In widening Karnaugh map, what Mirroring means? I can not understand the name of Mirroring, could you explain?
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question in Boolean algebra? [closed]

the question states: (Using Boolean Algebra; show that the following equation is valid: A'BC'D+(A'+BC)(A+C'D')+BC'D+A'BC' = ABCD+A'C'D'+ABD+ABCD'+BC'D RHS and using de Morgan law A'BC'D+(A'+...
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BCD and numbers [closed]

i should do a BCD numbers that has 2,3,6,8. I did it. Sometimes it asks me to do BCD that has 3,6,9. I lost my way with 3,6,9. How? As far as i did 2 is on binary 0010 the 3 is 0011 the 6 is 0101 i ...
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Karnaugh maps how i put them exactly

Hello i have issue how i locate the variables on karnaugh maps.I know what to do but i have the problem how i locate it.What i mean by that as you can see i have this: F=A'B'C'+B'CD'+A'BCD'+AB'C' ...
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minimize hazard free function

Given a function, e.g. \$y = f(x_0, x_1, x_2, x_3) = \sum m(0, 3, 4, 5, 6, 7, 8, 9, 11, 15)\$. How can i find the minimized function without hazards? I see this can be minimized using a Karnaugh map: ...
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Converting BCD Truth Table to Output Functions Using K-Maps

To be honest, I'm just looking to see if I'm on the right track with a certain question. This here would be my answer for the K-Map for the "H" output function and im just curious if im on the right ...
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Karnaugh Map race conditions with don't cares

Karnaugh maps show race conditions as adjacent minterms that are not covered in the same implicand. Take the following example: We have race conditions when moving from the blue implicand to the ...
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Simplification of boolean expression

I am asking you for a help with following boolean expression that i can't solve by myself. I can minimize expression in Karnaugh map but i have to use boolean algebra too. Expression: !(C + !D) * !(...
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finding if certain numbers are don't cares in KMAP

i've solved several question but i don't know how to solve this one, please help me if you can, as my due date is today. \$f(a,b,c,d)=\sum(0,1,2,4,5,10,12)\$ after a lot of trials, i know that this ...
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Order of writing variables at the top left of a K-Map

[Beginner here] I was studying from AAC and I've reached till here. On this page, they've this example: My confusion is NOT in how to make pairs, quads or octets or how to fill gray codes. I'm good ...
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Implementing 3 variable boolean function od 2-1 multiplexers

Recently i've been given a task from my lecturer to implement \$f=\sum(1, 3, 4, 5, 7)\$ on "2-bit multiplexers". That's it. I assume he meant 2:1 MUX. I've came up with following k-map... +------+--...
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Concerning truth table, Karnaugh map, cost and delay of a logic function

A logic function called \$defragment(n)\$ receives as its input \$n\$ bits, \$d[0],...,d[n-1]\$, and \$n\$ flags, \$v[0],...,v[n-1]\$, indicating whether the input is valid. The function returns only ...
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How to design a circuit that cycles

I want to design a digital circuit that transitions in the following sequence as follows: (0,0,0,0) -> (0,1,0,1) -> (0,0,0,0) -> (1,0,1,0) How would I go about making a k-map for this? Should I add ...
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karnaugh map and don't care states

I'm trying to figure out the boolean expressions I need for drawing a circuit based on a state transition table. I wound up with the k maps below, but I'm not really sure what to do with them. Would I ...
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Gray Code Conversion

I'm aware that in Gray code the successive numbers will differ only by one bit. However I'm not able to proceed further.
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Divide clock frequency by 3 with 50% duty cycle by using a Karnaugh Map?

In this document, On semiconductor describe how to design a divide by 3 system using a Karnaugh Map: ...
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What is the boolean expression?

I'm not sure how to tackle this problem. I think it might involve creating a logic table first. Please help! An elevator has the following sensors: G - The gate is closed L - The elevator is loaded. ...
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4 To 1 MUX - Figuring out the inputs

If i have a 2to1 mux together with logic gates like this: I can simply create a karnaugh map and test the different values of XYZ and get a function. From this i get the function f = x'z + yz + x'y ...
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How can I convert multiple Karnaugh maps into a logic gate circuit?

I'm designing a 8421 BCD to 84-2-1 BCD converter circuit. The truth table is: ...
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Is a Karnaugh map always a good way to simplify a Boolean expression?

I want to simply the following expression: (NOT A AND NOT B AND NOT C) OR (NOT A AND B) OR (A AND B AND NOT C) OR (A AND C) I created a truth table first, then a K map from the truth table. (See ...
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K Map, Essential prime Implicant

I have solved the above problem in two ways.And both the times I have a unique solution with the same number of gates. According to my understanding of Essential Prime Implicants, This particular ...
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How do I design a clocked synchronous state machine for a combinational lock?

I need help in completing a task, I’m stuck on quite a few things. Since I’m very new to this topic on finite machines. I’ve attempted the state diagram, state table, transition table, K-map values ...
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Solving 5 variables Karnaugh map - grouping with hazard

Welcome, according to topic Solving 5 variables Karnaugh map - grouping I would like to ask you if for this exercise, should I create anti-hazard group? Is it good? The solver http://www.32x8.com/ ...
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Solving 5 variables Karnaugh map - grouping

Welcome. I would like to ask about solving Karnaugh Maps, especially grouping 5-variables map. I am not sure if I made this good way, so if you could, please let me know what is wrong. It seems to me ...
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Excess-3 to binary decoder using unused combinations of the code as don't-care condition

This problem is from my textbook chapter review question, and it seems a lot different from the example provided by textbook, so I have no idea what to do. I even have solution manual for this, but ...
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Moore “01010” sequence detector

My task is to design Moore sequence detector. As my teacher said, my graph is okay. I wrote down next states, and outputs, then decided which flip-flops I'll use. With Karnaugh tables, I miminalized ...
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karnaugh map question

I have two JK-flipflops with outputs Q_1 and Q_2, with two extra input signals A_1 and A_2. They need to do the following (the truthtable just contains 3 examples, it's not complete): How do you make ...
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Sum of products or product of sums?

What does P indicate in this expression? F(A,B,C,D) = P(4,5,6,7,8,12,13)+d(1,15) And does d(1,15) represent don't care condition?
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If I had an infinitely large paper, how could I draw an n-element karnaugh map for (n>6)?

I understand that k-maps become impractical after around 5 variables, and my textbook only describes them up to 6. However, out of curiosity, is there a general rule, method, or algorithm that I could ...