9th Class Computer: chapter 6 Boolean Algebra Short Questions Answer
9th Class Computer: chapter 6 Boolean Algebra Short Questions Answer
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Boolean algebra is the algebra of logic. It is also called logical algebra or switching algebra. It was introduced by English mathematician George Boole in 1847. It use symbols to represent the logical statement instead of words. It consist of many rule to manipulate the symbols.
Boolean algebra is the tool to represent logical ideas in mathematical way. It is simplified analyzed and translated into real hardware for implantation by using logical gates.
The logical statement that either TRUE or FALSE is called proposition. For example the sentence “What is you address?” is not a proposition because its result is not in the form of TRUE or FALSE. However, the statement “Are you student?” is a proposition as its result is TRUE or FALSE.
The variable used in Boolean algebra is represent by different alphabets such as A, B, C…X, Y, Z. Each variable must take value 1 or 0. These value may be given different name to variables such as true or false, yes or no and on or off etc.
There are three operation can be perform in Boolean algebra. These are known as logical AND (x.y), logical OR (x + y), logical NOT (x).
AND operation is used to perform logical multiplication of two binary variable or constant. The AND operation is performed by using AND operator. AND operator is denoted by dot (.).
The OR in Boolean algebra is used to perform logical addition of two binary variable or constant. The OR operation is performed by using OR operator. OR operator is denoted by dot (+).
AND operation is used to perform logical multiplication of two binary variable or constant. It is denoted by dot (.). The OR operation is used to perform logical addition of two binary variable or constant. It is denoted by dot (+).
NOT operation is used the complement of two binary variables. A complement is the inverse of variable and it is denoted by bar over variable. NOT operation performed by NOT operator. It is denoted by bar placing above the variables.
A Boolean expression is logical statement that is either true or false. It consist of different elements of Boolean algebra such as Boolean variables, constant, logical expressions and parentheses.
The order in which is different type of operators of Boolean expression are evaluated is known as operator precedence. It is also known as hierarchy of operation.
A Boolean function is a expression that can be formed by binary variables, Boolean operators, parentheses and = sign. The value of Boolean variable can either 0 or 1. The value return by the Boolean function can also be 0 or 1.
x.x=x
A.(B+C)=(A.B)+(A.C)
Boolean function simplify by using the laws, rules and theorem of Boolean algebra. The simplified expression result is fewer expression and simper circuit. A simpler expression results is simple and efficient hardware. It require less number of logic gates that reduced the cost of production.
A truth table represent the output from different combination of input variables.
K-map very easy to follow. It is a systematic process to simplify Boolean expression. It is not scalable. It become complex for large number of variables.
