class 9 computer new book chapter 3 lecture 5 Construction of Boolean Functions скачать в хорошем качестве

class 9 computer new book chapter 3 lecture 5 Construction of Boolean Functions

class 9 computer new book chapter 3 lecture 5, Construction of Boolean Functions, class 9 computer new book chapter 3, 3.2.1.2 Construction of Boolean Functions Boolean functions are algebraic statements that describe the relationship between binary variables and logical operations. These functions are particularly important for digital logic design and are employed in formation of various digital circuits, which are the basis of current computers, mobile phones and even simple calculator. Understanding Boolean Functions: A Boolean function is a function which has a one or more binary inputs and produces a single binary output. The inputs and outputs can only have two values: False (represented by 0) and True (represented by 1). The construction of Boolean functions is done by employing the basic logical operations such as AND, OR and NOT, which connect the inputs to generate the correct output. Example 1: Simple Boolean Function Consider a Boolean function with two inputs, A and B. We can construct a function F that represents the AND operation: F ( A, B ) = A . B Outpu t Figure 3.2: Simple Boolean Function Input The diagram shown above demonstrates a basic digital circuit, which is an AND gate. The box symbolizes the AND function F (A, B) = A . B. This box has two inputs A and B. If both A and B are 1, the output will be 1. In any other case, the output will be 0. The input are shown at the entrance to the box, while the output is depicted at the exit of the block. The truth table for this function is as follows: 56 Table 3.4: Truth Table for F(A,B) = A.B A B F(A, B) 0 0 0 0 1 0 1 0 0 1 1 1 Example 2: Now, let us construct a more complex Boolean function with three inputs, A, B, and C: F (A, B, C) = A . B + A . C This function uses AND, OR and NOT at the same time. The truth table for this function is as follows: Explanation: • The parameters A, B, and C are included in the following example as the input columns. • The results of AND operation between two variable A and B are presented in the column A · B. • The column A standing for the NOT operation of A. • Every value in the column A · C displays the result of AND operation between the values in the Fifth column and the third column. • The final column F (A, B, C) shows the output of the Boolean function (A . B) + (A . C) Table 3.5: Detailed Truth Table for F (A, B, C) = (A . B) + (A . C) A B C A·B A A· C F(A, B, C) 0 0 0 0 1 0 0 0 0 1 0 1 1 1 0 1 0 0 1 0 0 0 1 1 0 1 1 1 1 0 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 1 0 0 1 1 1 1 1 0 0 1 Usage in Computers: There are many uses of Boolean functions in the computers for various operations. Here are some examples of their usage: • Arithmetic Operations: Boolean functions are used in Arithmetical Logic Units (ALUs) of CPUs to perform operations like addition, subtraction, multiplication, and even division. 57 • Data Processing: Boolean functions are used to process binary data in memory and storage devices, ensuring efficient data manipulation and retrieval. • Control Logic: Boolean functions are applied in computers to control various parts of the system's operation to function in co-ordinated manner. cs by sam,class 9 computer new book chapter 3 lecture 5,Construction of Boolean Functions,class 9 computer new book chapter 3,9th computer new book,class 9 computer new book 2025,boolean function,boolean statements,understanding boolean function,define boolean function,how boolean function construct,construction of boolean function,computer new book class 9,computer new book unit 3 boolean function,boolean variable,chapter 3 computer new book class 9,class 9 #class9computernewbookchapter3 #booleanfunction #constructionofboleanfunction #csbysam #everyone #everyday