Boolean Algebra Rules Boolean Algebra provides a basic logic for operations on binary numbers 0, 1. Since computers are based on binary system, this branch of Mathematics is found to be useful for the internal working of various computers. The application of Boolean algebra to electronic devices such as computers, lies in the restriction of the variable to two possible condition 'On and Off' or 'True or False' or numerically '1 or 0'. The electric circuits carry out the Boolean logic. In practice, electronic engineers use the language of logic as follows. They use the symbol '1' to refer the values of the signals produced by an electronic switch as 'On' or 'True'. They use the symbol '0' to refer the values of the signals produced by an electronic switch as 'Off' or 'False'. The symbols 0 and 1 are called bits. Know More About Standard Form in Math
Boolean Operators Boolean algebra is closed under AND, OR and NOT operations. A boolean operators that define relationship between a word and a group of words. But this operators are used in logical operation with switching circuits. Logical OR operation Logical AND operation Logical NOT operation We associate two logical operations 'AND' and 'OR' operations with switching circuits in 'series' and 'parallel' respectively. Let us refer to a circuit consisting of two switches p and q connected in series with a lamp and battery as shown in figure. The lamp will glow, only if switch p and switch q are closed. If we replace the word 'closed' by T and 'open' by F, the switch will glow only if p = T and q = T. In binary language, we say the switch will glow if p = 1 and q = 1. Table 1, Table 2 and Table 3 describes all possible states of the switches for the series connection.
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Logical NOT Operation The logical NOT operation is right associative and although it would produce the same result using either left or right associative property because it is a unary operator having only a single operand. This operation has one input and one output. Table 7 represents truth table for NOT operation. Note that the 'NOT' operation is a unary operator, whereas 'AND' and 'OR' operators are binary operators. We have already discussed what a Boolean function is. Here is a formal definition for Boolean expression and Boolean function.
Linear Equations with Fractions Learn about solving linear equations with fraction. In a linear equation the degree of the equation will be always one. It contains variables and constants and contain a first power of variables, also does not contain product of two variables. A linear equation may contain one or more variables in it. Linear equation is a simple equation. It has lots of application in mathematics and many other fields. Solving a equation is finding the value of unknown variables in the equation. The equation involving fraction contains terms of the form . Here the method to solve is by taking the fraction term to one side and taking least common multiple(LCM) and them cross multiply the equations bring terms with variables to one side and constants to other side. Take variable common and then take remaining term to other side and simplify them.Now we will see some examples of solving equations with fraction below.
Solving Equations with Fractions Below are the examples on solving linear equations with fractions Example 1: Solve the linear equation = 3 Solution: Step 1: Given equation =3 Step 2: Multiply by 4 on both sides Ă—4=3Ă—4 y = 12 Example 2: Solve the linear equation + 5 = 9 Solution: Read More About What is an Independent Variable
Step 1: Given equation +5=9 Step 2: Subtract 5 on both sides of the equation +5-5=9-5 =4 Step 3: Multiply by 3 on both sides of the equation ×3=4×3 x = 12 Example 3: Solve the linear equation + = 4 Solution: Step 1: Given equation + =4 Step 2: Add the fractions and
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