"The Building Blocks of Digital Systems". This title highlights their fundamental role in digital electronics and computer architecture.
- 1. Logic Gate By : HASAN SAIYED
- 2. Contents Introduction Basic Concept Type of Logic Gate Conclusion
- 3. Introduction : Boolean Logic Boolean Algebra is algebra of logic which deals with the study of binary variables and logical operation. As every data are represented in terms binary values, we need to manipulate those values by using some certain rules and expression which we can do through Boolean Algebra. Boolean logic, also known as Boolean algebra, is a form of algebra that deals with true and false values, using operators like AND, OR, and NOT to perform logical operations, which are fundamental to how computers make decisions.
- 4. Basic Concept Boolean Variables : A Boolean variable is a variable that can only hold one of two values: true or false, often represented as 1 or 0, forming the basis of Boolean algebra and logic gates. Boolean variable: Those entities which has either or 0 and 1 and denote some specific operation ore known as boolean variable. Simply, it is an entity in Boolean algebra which has only either of the two possible values. This variable are denoted by A, B, P, Q, X, Y, Z…. Boolean function (logic functions): Boolean function is an expression formed by binary variables, F = XYZ’+XY Where, F is a boolean function X, Y, Z are a boolean variable.
- 5. Truth Table: A table which represents the input-output relationship between of the binary variables for each logical gate called truth table. It shows the relationship between input and output in tabular form. Thus, truth table is table representing the results the logical operation of the logical operation on all possible combination of logical values. Boolean Operator and Operands : Operators are the symbols that define the specific operation. These are three basic operators used in Boolean Algebra, i.e. AND, OR, NOT. Every other operations can be expressed in terms of this basic operation. For examples, NOR operator is the combination of NOT and OR operators.
- 6. Types LOGIC GATES: The Types of logic gates are: AND, OR, NOT AND Gate : AND operation is also known as logical multiplication. It is an electronic circuit, which produce high logic (1) output when both the input logic are high (1) and produce low logic(0) when any one of the input logic is low (0). AND operation is represented by (.) dot operator. also represented by AˆB or AnB. Truth Table Algebraic expression: F=A.B where, A and B are inputs, F is an output. INPUT OUTPUT A B F=A.B 0 0 0 0 1 0 1 0 0 1 1 1
- 7. Graphical Symbol, Circuit Diagram and venn diagram:
- 8. OR Gate: It is an electronic circuit, which produce high logic (1) output when any one of the input logic are high (1) and produce low logic(0) when both the input logic is low (0). The output produce by this basic gate is the sum of its input logic. Algebraic expression: F=A+B where, A and B are inputs, F is an output. Gate Symbol : Venn-Diagram :
- 9. Truth Table : INPUT OUTPUT A B F = A+B 0 0 0 0 1 1 1 0 1 1 1 1
- 10. NOT Gate : It is an electronic circuit, which produce high logic (1) output when the input logic is low (0) and produce low logic(0) when the input logic is high (1). The output produce by this basic gate is the reciprocal of its input logic. Algebraic expression: F=A’ where, A is inputs, F is an output . Gate Symbol : Venn diagram :
- 11. Truth Table : INPUT OUTPUT A F = A’ 0 1 1 0
- 12. NAND GATE : It is the combination of NOT and AND gate, which produce high logic (1) output when any one of the input logic is low (0) and produce low logic(0) when both the input logic is high (1). The output produce by this basic gate is the reciprocal or complement of AND gate. It is also known as derived gate. Algebraic expression: F=(A.B)’ where, A and B are inputs, F is an output. Gate Symbol : Venn diagram :
- 13. Truth Table : A B A.B F = (A.B)’ 0 0 0 1 0 1 0 1 1 0 0 1 1 1 1 0
- 14. NOR Gate : it is the combination of NOT and OR gate, which produce high logic (1) output when both the input logic is low (0) and produce low logic(0) when any one of the input logic is high (1). The output produce by this basic gate is the reciprocal or complement of OR gate. It is also known as derived gate. Algebraic expression: F=(A+B)’ where, A and B are inputs, F is an output. Gate Symbol : Venn diagram :
- 15. Truth Table : A B A+B F = (A+B)’ 0 0 0 1 0 1 1 0 1 0 1 0 1 1 1 0
- 16. X-NOR Gate: it is derived gate, which produce high logic (1) output when both the input logic are either high (1) or low (0) otherwise it will produce low logic(0). Algebraic expression: F=A.B+A’.B’ where, A and B are inputs, F is an output. Gate Symbol : Venn Diagram :
- 17. Truth Table : A B A’ B’ A.B A’.B’ F = A.B+A’.B’ 0 0 1 1 0 1 1 0 1 1 0 0 0 0 1 0 0 1 0 0 0 1 1 0 0 1 0 1
- 18. X-OR Gate : It is derived gate, which produce low logic (0) output when both the input logic are either high (1) or low (0) otherwise it will produce high logic(1). Algebraic expression: F=A’.B+A.B’ where, A and B are inputs, F is an output. Gate Symbol : Venn Diagram :
- 19. Truth Table : A B A’ B’ A’.B A.B’ F = A’.B+A.B’ 0 0 1 1 0 0 0 0 1 1 0 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 0 0