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Questions tagged [karnaugh-map]

The Karnaugh map provides a simple and straight-forward method of minimising boolean expressions. With the Karnaugh map Boolean expressions having up to four and even six variables can be simplified.

A Karnaugh map provides a pictorial method of grouping together expressions with common factors and therefore eliminating unwanted variables. The Karnaugh map can also be described as a special arrangement of a truth table.

Karnaugh maps can be used to simplify expressions

For example:

Karnaugh map example

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Proving non-optimality of a Karnaugh map

I would appreciate some help in finding literature specifically addressing K-map optimality. I understand how, for example, you can map between SOP (sum-of-product) expressions and a K-map, and why in general you would expect the K-map optimized…
user1623303
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Digital Logic - Karnaugh Map

The initial problem starts like this. There are 6 states. At each state when w=1 move to the next state, when w=0 then stay at the current state. At each state display a number using a standard 7 led display (BCD). Those numbers are 8 -> 1 -> 9 -> 4…
CMacDady
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Detecting XOR in Karnaugh Maps

I got the following Karnaugh Maps but I am still having problems working out the expression for XOR from each table. Table 1 ------- WZ 00 01 11 10 ----------------------- …
Hakim Marley
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Why can't brackets in a simplified Boolean expression be separated by an AND?

Consider this map of (A ∧ D) ∨ (B ∧ D) ∨ (A ∧ ¬B ∧ C ∧ D): The map is grouped into two sections, both of four squares. Thus producing the simplified expression of (B ∧ D) ∨ (A ∧ D) as shown below. This is in following with the rule: "Groups must…
Montresor
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How to convert many-valued logic into efficient boolean logic?

Suppose that I have a set S consisting of {0₁, ¯1₂, 0₂, 1₂, ¯2₃, ¯1₃, 0₃, 1₃, 2₃, ¯3₄, ¯2₄, ¯1₄, 0₄, 1₄, 2₄, 3₄}. I want to define the following operations over S: S < 0 which returns one if and only if S is negative. ¯S which returns the negation…
Aadit M Shah
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Constructing truth table headings in boolean logic with Java

I am working on a small project to construct truth table based on an infix boolean logic expressions. Example: A ∧ (B ∨ C) I am able to convert this to postfix: ABC∨∧ and thus am able to construct the expression into a binary tree (can convert the…
alistaircol
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Simplify boolean expression using Karnaugh map

I have the following problem: Express the following boolean expressions as sums of products and simplify as much as possible using a Karnaugh map I drew the Karnaugh map and then placed my values in the table as true (First one, B non D meaning…
Diana
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How to understand this style of K-map

I have seen a different style of Karnaugh Map for logic design. This is the style they used: Anyone knows how this K-Map done? How to comprehend with this kind of map? Or how they derived from that equation from that map. The map is quite different…
Jay Marz
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Boolean logic - simplifying sum of products

I've got a question that asks to synthesise the simplest possible sum of products expression for a given function. Basically the function is 1 if AB == CD, and 0 otherwise, which works out like this: (!A && !B && !C && !D) || (!A && B && !C && D) ||…
user1432402
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What are the advantages/disadvantages of using the karnaugh map instead of the truth table

What should I use? Or are there special occasion where I should use one over the other?
jantristanmilan
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Creating a list of possibilities from splitting strings at a certain character - Karnaugh Map

I am trying to create "truth tables" for use in a Karnaugh map solver. The Karnaugh Map solver takes in the settings of the variables ABCD as a string of 4 numbers representing what they are set to. For example, ABCD could be anything from "0000" to…
Alenna Spiro
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When do Karnaugh Map terms make no groups?

I understand how K-Maps work and what their utility is, but I can't seem to figure out under what conditions there could be no groups made. (When an expression is not simplifiable further? Won't it always be while speaking of canonical terms?) Do…
Arnav Das
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Algorithm to simplify kv map with more than 4 variables

does someone know an algorithm to simplify a kv map with more than 4 variables. With 4 variables you just creat groups of field that are near each other. And than you can write down the logic expression that discribes this group. By doing this for…
leet
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K-Map to solve algebraic reduction

I need help verifying an algebraic expression using K-Map. The expression I'm posting was actually done by my professor, but for practice purpose I wanted to use the K-Map to verify that the answer is correct. -> X • Y + X' • Y • Z' + Y • Z = …
miiworld2
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Making K-maps with S2, S1, S0 (seven states), one button input, and four outputs

So my state diagram has seven states (000 to 110), an input B button, and four outputs P, Q, R, and S. I've made the truth table, which has 16 rows (two of which have Xs). I'm supposed to make 7 K-Maps out of this, S2' S1' S0' P Q R and S. I…
sumitz1212
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