There are 4 variables in the Boolean function and the value of the function is 1. Find the number of cells in the K-Map which will contain a 1 when SOP expression is used.a)12b)0c)16d)14e)1Correct answer is option 'C'. Can you explain this answer?

Question

Answer

Concept:
The K-map is a graphical method that provides a systematic method for simplifying and manipulating the Boolean expressions or to convert a truth table to its corresponding logic circuit in a simple, orderly process.
In an 'n' variable K map, there are 2n cells.

Application:
For 4 variables there will be 2⁴ = 16 cells
The K map will give an output of 1, when all the cells have a 1, i.e. if all the input combinations give an output of 1, the maximum number of inputs can be simplified to give an output of 1.
This is explained with the following K map:

Since the K map forms a pair of 16, it can be eliminated giving an output:
Y = 1
Since the output contains no input variables (A, B, C, or D), all the four variables are simplified/eliminated.

Answer

To solve this problem, we need to use a Karnaugh Map (K-Map) to simplify the Boolean function and find the number of cells that contain a 1.

Step 1: Determine the Number of Variables
The problem states that there are 4 variables in the Boolean function.

Step 2: Create the K-Map
Since there are 4 variables, we need a 4-variable K-Map. This K-Map will have 2^4 = 16 cells.

Step 3: Fill in the K-Map
We are given that the value of the Boolean function is 1. We need to determine the cells in the K-Map that correspond to this value. To do this, we can use the Sum of Products (SOP) expression.

The SOP expression is a Boolean expression that represents the logical OR of multiple AND terms. Each AND term consists of a combination of variables that results in the function being equal to 1.

Step 4: Determine the SOP Expression
Since the value of the function is 1, the SOP expression will consist of terms where the variables are in their complemented form (indicated by a bar over the variable). In other words, the terms will contain the variables in the form of A'B'C'D', where A', B', C', and D' represent the complement of variables A, B, C, and D, respectively.

Step 5: Identify the Cells with 1
To identify the cells in the K-Map that contain a 1, we need to look for the groups or clusters of adjacent cells that correspond to the terms in the SOP expression. Each group should have a power of 2 number of cells (1, 2, 4, 8, etc.).

By examining the SOP expression and the K-Map, we can see that there is one group of 16 cells that contains a 1. Therefore, the answer is option 'C' - 16 cells.

Similar Electrical Engineering (EE) Doubts

Consider the following Boolean function with four variables f(w,x,y,z) = Σ(1,3,4,6,9,11,12,14).The function is

Without any addition circuitry, an 8:1 MUX can be used to obtain.

A 4 × 1 MUX used to implement a 3-input Boolean function is as shown above. The Boolean function F(A, B, C) implemented is

With 4 Boolean variables, how many Boolean expressions can be formed?

Top Courses for Electrical Engineering (EE)View all

Network Theory (Electric Circuits)

GATE Electrical Engineering (EE) Mock Test Series 2025

General Aptitude for GATE

GATE Notes & Videos for Electrical Engineering

Engineering Mathematics

Top Courses for Electrical Engineering (EE)

Top Courses for Electrical Engineering (EE)

Suggested Free Tests

Related Content

Mock Test Series

Subject-wise Courses

Subject-wise Courses

Other Engg Branches

Company