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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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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Dont care condition-Karnaugh map

I am a bit confused with dont care condition. I understand that in a system they are the positions that they dont affect they output when they are either High or Low. How about this, F=A'.D'+B'.C'+A'....
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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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Task:Design a“Disinfection Chamber”. Solved it using s-r latches. However, since it was not taught, it was not allowed. How to solve this without it?

Here is my design: I was asked to design a digital circuit of "Disinfection Chamber" (Below). I solved it using 2 s-r flip-flop. But apparently, I can't use flip-flop because it hasn't been taught. ...
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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 ...
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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 ...