Question

find reduced expression for the function F(A, B, C, D) = sigma m (0, 1,3,5,6,7,10,14,15) using kmap​

Answer 1

Explanation:

All About Circuits

Pages in Chapter 8

Introduction to Karnaugh Mapping

Venn Diagrams and Sets

Boolean Relationships on Venn Diagrams

Making a Venn Diagram Look Like a Karnaugh Map

Karnaugh Maps, Truth Tables, and Boolean Expressions

Logic Simplification With Karnaugh Maps

Larger 4-variable Karnaugh Maps

Minterm vs Maxterm Solution

Sum and Product Notation

Don’t Care Cells in the Karnaugh Map

Larger 5 & 6-variable Karnaugh Maps

What is the symbol of sum of minterms?

Σm

Sum and Product Notation

Chapter 8 - Karnaugh Mapping

PDF Version

For reference, this section introduces the terminology used in some texts to describe the minterms and maxterms assigned to a Karnaugh map. Otherwise, there is no new material here.

Terminology for Minterms

Σ (sigma) indicates sum and lower case “m” indicates minterms. Σm indicates sum of minterms. The following example is revisited to illustrate our point. Instead of a Boolean equation description of unsimplified logic, we list the minterms.

f(A,B,C,D) = Σ m(1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 13, 15)

or

f(A,B,C,D) = Σ(m1,m2,m3,m4,m5,m7,m8,m9,m11,m12,m13,m15)

The numbers indicate cell location, or address, within a Karnaugh map as shown below right. This is certainly a compact means of describing a list of minterms or cells in a K-map.

Karnaugh map sum and product notation

The Sum-Of-Products solution is not affected by the new terminology. The minterms, 1s, in the map have been grouped as usual and a Sum-OF-Products solution written.

Terminology for Maxterms

Below, we show the terminology for describing a list of maxterms. Product is indicated by the Greek Π (pi), and upper case “M” indicates maxterms. ΠM indicates product of maxterms. The same example illustrates our point

Answer 2

Answer:

The Boolean Expression for k-map is F(A, B, C, D) = A’BC’ +’ A’CD + AB’D + ABD’+C’D.

Explanation:

• A K-map is known as karnaugh map which is method used to reduce or minimize the given Boolean Expressions without using Therorems of Boolean algebra or manipulation of the Equation.

• There are different types of K-map. They are:

1) 2 variable K-map

2) 3 variable k-map

3) 4 variable K-map

4) 5 variable K-map

Given that:

F(A, B, C, D) = sigma m (0, 1,3,5,6,7,10,14,15) using k-map

To find:

The Boolean expression for K-map =?

Solution:

There are 4 pairs and 1 Quad which will be reduced:

From the diagram, we can understand that:

For Pair-1(m4 + m5) reduces to A’BC’  

For Pair-2(m7 + m13) reduces to A’CD

For Pair-3(m9 + m11) reduces to AB’D

For Pair-4(m12 + m14) reduces to ABD’

For Quad(m1+ m5 + m9 + m13) reduces to C’D

Therefore, when we simplify the Boolean expression for given K-map is F(A, B, C, D) = A’BC’ +’ A’CD + AB’D + ABD’ + C’D.

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