# 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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### How do I decompose 6 or more variable truth table to groups of 4 or 3 variable truth table and K-map them and combine the equations?

K-maps are a go to method of finding SOP/POS form for truth tables of up to 4 variables, beyond that the K-maps become explosively complex to manually draw and solve. Is it possible that for 6 bit ...
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### Building a circuit which adds 2 signed numbers

I am developing circuitry to add 2 numbers with sign.They have the form: $$b_{1}:(sign)|(absoluteval)$$ I realised that the calculation of the sign of the addition of such 2 binary numbers must be ...
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### Converting this boolean expression to NOR only expression

I was given an expression which I simplified using k-maps to obtain the following: ~WY + W~YZ + ~W~X~Z I followed along with some of the other workings people have done for converting functions, but ...
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### How can I make sure I have reached the simplest result by using K-map

I know how to simplify a circuit by using the K-map. However, I am still curious whether my result is the simplest. I have heard that when using K-map, try using the biggest and the fewest loops. But, ...
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1 vote
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### Find static 0 hazard

In this question, the top F=A'C'D' + A'B'C + ACD' + AB'C' is given in the question. With the question, im able to generate the kmap. Then in the kmap, i find F'=A'C'D + A'BC + ABC'+ ACD. To remove the ...
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### How to fill in k-map with values from an finite state machine table?

I'm struggling to understand how I am supposed to fill in this k-map with the help of this finite state machine table? I understand that q1q0 shows the present state but I don't understand how I am ...
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### simplify Boolean function F(A, B, C, D) = ∑ m(0, 1, 3, 4, 5, 7,8,9 11, 13,14,15)

Hello just got stuck simplifying this boolean function using four variable K-Map. I have to simplify this boolean function in terms of sum of minterms. ...
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### Need help understanding multiplexer (MUX) inputs and K-map combinations

I'm trying to understand multiplexers (MUX) and I have a few questions that I hope someone can help me with. I'm not sure what determines if the inputs to the MUX are multiplications (AND) or ...
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1 vote
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### Did I create this Karnaugh map correctly?

I'm tasked with making a 4-7 decoder for a 7-segment LED (common anode). I am an extreme layman (1st year EEE student) I have 4 inputs (A,B,C,D) ...
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### Trouble with FSM circuit using Schmitt trigger clock

I'm having some trouble with my circuit based on the design below, that I built for the lab. I'm using a Schmitt trigger clock. I built the circuit on a breadboard and connected it to the clock and ...
1 vote
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### Kmap and boolean equation for a function

F(A,B,C,D) = Σm(1, 2, 4, 6, 8, 10, 11, 13, 15) Here's my try of the kmap: Are my kmap and boolean equation correct for this function?
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### How do I write the expression based on a combinational analysis? [closed]

I don't understand how to write the expression based on a Karnaugh map, can anyone help?
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### Minimizing a Boolean Expression

From a 3 variable K-map I get the following expression: BC + B!C! *!=not I know that a + a!b = a, so does this mean that BC + B!C! = B + C?
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### Will the Karnaugh diagram change when you use gray code on the truth table?

I am currently trying to put this state diagram into a truth table: I wrote the truth table like this: When I try to get the expression for q1+ I get: q1+ = q1q0' + q1q0x, but I can apparently get: ...
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### Implying a boolean function by using 5 NANDS only - How to implant "1" using nand?

Function: f(a,b,c,d) = b' + c' + ad + a'd' I used Karnaugh map (4x4). Received that the function is all squares except square number 7 (there it is 0). Which means: Now what is the problem? When I do ...
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### Is Quine–McCluskey algorithm globally optimal or is there a better way for K-Map reduction?

A bit of context... We are working on a project to convert FA (Finite Automata) to Digital Sequential Circuits and vice-versa. In this process we came across a step: Reduction of Karnaugh (K-Maps). ...
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### Is this a static 1 hazard?

Here the minterms of the SOP representation are ~A~C + AC (XNOR gate). However is there a static 1 hazard between the two terms? When the expression changes from ~A~C to AC, there could be small ...
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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?
1 vote
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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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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 ...
1 vote
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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 ...
1 vote
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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?
1 vote
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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 : ...
1 vote
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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),...
209 views

### 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 I convert a Karnaugh map into a logic gate circuit?

I currently have some questions that I need to work out in uni. I've been given 2 lengthy boolean expressions and I need to simplify them. Question a I feel like I've done right but question b I'm ...
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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 ...