# 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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### What is d in a boolean function?

I know if it's $\Sigma$ we put 1's in the Karnaugh map, but I don't know what $d$ is. $$f(a,b,c,d) = \Sigma m(0,1,4,10,15) + d(7,14)$$ From what I've googled, https://en.wikipedia.org/wiki/...
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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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### Moore state machine and Karnaugh map of output

In the Moore state machine if we want to find the output we create a Karnaugh Map of present states and input. Why? The output of the Moore machine by definition doesnt depend on the input so we ...
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### 4-variable Karnaugh map

I would like to ask if I grouped this Karnaugh map correctly and if the equation is correct. I'm not really sure if it's right so if it's not, how can I correctly group this? And please let me know ...
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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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### Minimize the switching function from Karnaugh map

I need to minimize the switching function y=f(x1,...,x5) represented by the Karnaugh map. I wonder if I did it in the right way. Can anyone check this?
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### Grouping for 5 variable k-map

Below is the K-map for 5(ZABCD) variables for a particular output namely Jb. Noticed the "1" I highlighted, how should I group them? The "x" represent don't care term. Should 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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### Please help solve my kmap

I've been scratching my head for a few hours over my issue. [ This is my kmap i am trying to solve and simplify This is my working soltion ~Q3 & ~Q2 & ~Q1 & Q0 & x & y || ~Q3 & ...
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### Confused About the K-MAP Minimization

I want to Construct a priority encoder which implements the encoding of 0,3,1,2 with descending priority (i.e. 0 has the highest priority and 2 has the lowest. but i am confused about my KMAP I am ...
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### Karnaugh map: What values to combine?

I have obtained the Karnaugh diagram (pictured below) and now I'm trying to obtain the Boolean expression of K3 through this diagram. My inputs are Q1, Q2 and Q3. I'm trying to "group" 1's ...
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### Reducing the Number of Logic Gates in a NOR-driven 7 Segment Display

I have been given a prompt to design a 7 segment display using NOR gates. My understanding of the prompt (8.R) is: Design an excess-2 code converter to drive a 7 segment display. Design the display ...
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### How do I turn a 4-variable k-map with don't cares into a simplified boolean expression?

The trouble I'm having here is that I don't know a method (well I do know I could do it the long way i.e w'x'y'z' + w'x'y'z . . .) for turning this into a simplified boolean expression. I've done some ...
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### Is my redundancy identification and K-Map grouping correct?

(Problem 7). Am I correct in saying that (m2, m6) the one circled in purple on the k-map is redundant? Also, if that is the case, how do I remove it from the boolean expression? I mean I turned that ...
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### Is the disjunctive normal form unique?

As the title says, is the DMF always unique? And if no, is there an example of a function that has more than one DMF?
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### Finite State Machine made of JK Flip Flops in Logisim help [closed]

I'm trying to make a 4 bit finite state machine that prints out (2, 3, 5, 7, 11) in order. I have completed the next state table, flip flop transition table and the JK Karnaugh maps for all the bits. ...
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### Is this K-map grouping legal?

Can the following K-map be grouped with 1s in the corners of a subsection of a 16-cell K-map?
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### Using don't cares to reduce a function

We have the function: f = p'c' + pb' + qc With satisfiability don't cares given by SDC = {pb, q'b', qbc, q'*c'} The K-map for the function is : ...
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### Simplifying boolean equations with K-map

My professor told me that I could arrive at the simplified solution using the K-map, which I guess I did, however it does not seem correct. The equation and corresponding solution are shown in the ...
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### A Counter Which Counts Two Different Sequences

I have a question which asks me to design a counter which counts two different sequences. The question goes like this: Design a counter which counts 0,4,6,8,12,14. When the counter reaches 14, it is ...
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### How can I construct a Karnaugh map from this table made from a Moore FSM Transition diagram?

I am new to Karnaugh maps and I would like to find out how I can go about this the data is correct but maybe the layout of this table is not correct, there are four states s0s1s2s3 and the inputs are ...
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### Building a T flip-flop with enable and reset using only a JK flip-flop that has no enable or reset, and use some necessary logic gates

I am confused about whether if I should use don't cares to fill in the J and K on the state table, or just use keep and change. If I use don't cares I will not get any Q inputs (as seen on the K-maps),...
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### Don't care condition in Karnaugh map

I am a bit confused with "don't care" condition. I understand that, in a system, they are the positions that don't affect the output no matter whether they are high or low. How about this: F ...
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### problem regarding karnaugh map

I can't understand how decimal designation differ by power of 2??
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### Design a 4-bit binary counter using D flip-flop

I am learning logic circuit now.I am going to design a 4-bit binary counter with D-flip-flop.It counts from 0 to 15.And when the number reaches 15,the number wont change and remains 15.I am now ...
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### State Table & Karnaugh-map for Finite State Machine

I am trying to create a Finite State Machine that is able to check if a number string is valid. For example, it would accept 3, 4.65 or 8.93e-10. So far I have created a transition table for the ...
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### KMAP Sum of Products - How to get the Simplified Function from the KMAP Table

I am answering a KMAP Sum of Products with don't care table but I don't know how to get the simplified function. Here's my progress: Problem: Q(C, O, D, E) = Σ(0,1,2,3,7,8,10) + d(5,6,11,15) The ...
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### Can anyone help me understand how to implement a karnaugh map using multiplexers in logism?

I am quite confused on how to implement a function using multiplexers. I know how to use a karnaugh map and get the necessary minimized function that I need, but I don't know how to implement it in ...
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### Logic operation on Karnaugh Maps?

Question: Normally I find Karnaugh Map of an expression from its truth table, but can we have Logic operation on two Karnaugh Maps ? Update:
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### How to obtain POS from the Karnaugh map?

I know there is a way of getting both without having to draw two maps, which is to draw the minterms on the map and then the Maxterms and organize them in groups just like the minterms. My question ...
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### Mapping XOR expression into K map

I know any SOP and POS can be minimised directly with the help of KMAP and there is no difficulty in mapping each Boolean product or sum term into KMAP. However what if the boolean expression is in ...
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### How do you fix the glitches in the following Karnaugh maps?

The following circuit is supposed to output 1 if the input is greater or equal than 1010 (decimal 10). The truth table is given and we are supposed to convert that to POS and SOP using Karnaugh maps. ...
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### Finding a minimal cost function from a Karnaugh Map

Below is a problem I made up and did. Is my solution wrong? Problem: Attached is following map for the function $f$. We want a minimal cost expression using only and, or and not gates. The cost ...
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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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### 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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### 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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### 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 ...