Consider the following statements regarding Boolean functions : 1. Each one of the product terms in the canonical SOP form is called a minterm. 2. Two squares in K-map are said to be adjacent to each other, if their min (max) terms differ in only one variable. 3. The binary number designations of the rows and columns of K-map are in Gray code. Which of the above statements are correct?
To determine which statements are correct regarding Boolean functions, let's examine each statement:
- Each one of the product terms in the canonical SOP form is called a minterm.
Explanation: In Boolean algebra, the Sum of Products (SOP) is a standard form of representing a Boolean function. A canonical SOP expression is one where each product term is a minterm. A minterm is a product (AND operation) of all the variables in the function, each of which may appear in true or complemented form. Thus, statement 1 is correct.
- Two squares in K-map are said to be adjacent to each other, if their min (max) terms differ in only one variable.
Explanation: In a Karnaugh map (K-map), adjacency between squares is determined by how the binary representations (or minterms/maxterms) of the squares differ. Two squares are considered adjacent if there is a difference in only one bit, which means one variable changes state between them. Thus, statement 2 is correct.
- The binary number designations of the rows and columns of K-map are in Gray code.
Explanation: Gray code is used in K-maps to ensure that adjacent squares differ by only one bit. This simplifies the process of combining terms to minimize the Boolean expression. The rows and columns are, therefore, arranged using Gray code. Thus, statement 3 is correct.
Conclusion: Since all three statements are accurate interpretations of concepts in Boolean functions and K-maps, the correct answer is 1, 2, and 3.
Important Questions from Logic Gates and Boolean Algebra
The number of distinct Boolean expressions of four variables is-
Which of the following types is best suited to represent the logical values?
In the given circuit, if the input voltage lies between +E1 and -E2, then output is zero.
Input and output characteristics are shown below.
The region between +E1 and -E2 is known as _____.
The minimum number of 2-input NAND gates required to realize the logic function $Y = AB + \bar A \bar B$ is
A*B*A, where * represents XOR, is equal to:
