Logic gates
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- The document describes several types of basic logic gates - inverter, AND, OR, NAND, NOR, XOR, and XNOR. - Each logic gate is defined by its truth table and logical expression showing the output for all combinations of inputs. - Complex logic gates can be constructed by combining simpler gates, such as using two-input AND gates to create a three-input AND gate.
Logic gates
- 1. LOGIC GATE • Actually the term logic is applied to digital circuits used to implement logic functions. Several kinds of digital logic circuits are the basic elements that form the building blocks for such complex digital system as the computer. • The lines connected to each symbols are the inputs and outputs. • The inputs are on the left of each symbol and the output is on the right. • A circuit that performs a specific logic operation (AND, OR) is called a logic gate.
- 2. THE INVERTER • The inverter (NOT circuit) performs the operation called inversion or complementation. • The NOT operation changes one logic level to the opposite logical level. When the input is Low, the output is high. When the input is high, the output is low. • The inverter changes one logic level to the opposite level. In terms of bits, it changes a 1 to a 0 and 0 to 1.
- 3. TRUTH TABLE OF INVERTER Input Output 0 1 1 0 When a High level is applied to an inverter input, a Low level will appear on its output. When a Low level is applied to its input, a High will appear on its output. LOGICAL EXPRESSION OF INVERTER X = A’
- 5. THE AND GATE • An AND gate can have two or more inputs and performs what is know as multiplication. • The output of AND gate is high when all inputs are high otherwise all outputs are low.
- 6. OPERATION OF AND GATE • An AND gate produces a HIGH output only when all of the inputs are HIGH. When any of the inputs is LOW, the output is LOW. Therefore, the basic purpose of AND gate is to determine when certain conditions are simultaneously true, as indicated by High levels on all of its inputs, and produces a High on its output. Inputs Output A B X 0 0 0 0 1 0 1 0 0 1 1 1 Logical Symbol Truth Table
- 8. LOGICAL EXPRESSION • It’s logical expression is, X=A.B X=ABC A B X=AB
- 9. FOR THREE INPUT AND GATE INPUT OUTPUT X Y Z O=X.Y.Z 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 0 1 1 1 1
- 10. THREE INPUT AND GATE USING (2/1 AND GATES)
- 11. • To determine the total number of possible combination of binary inputs to a gate is determined by the following formula. N=2n Where N is the number of possible input combinations and n is the number of input variables. Example, Two inputs variables; N=22 = 4 Combinations. Three inputs variables; N=23 = 8 Combinations. Four inputs variables; N=24 = 16 Combinations.
- 12. THE OR GATE • OR gate can have two or more inputs and performs what is known as logical addition. • The output of OR gate is Low when all inputs are low, otherwise all outputs are high
- 13. OPERATION OF AN OR GATE • An OR gate produces a High on the output when any of the inputs is High. The output is Low only when all of the inputs are Low. Therefore, an OR gate determines when one or more of its inputs are High and produces a High on its output. Logical Symbol Inputs Output A B X 0 0 0 0 1 1 1 0 1 1 1 1 Truth Table
- 15. LOGICAL EXPRESSION • It’s logical expression is, X=A+B A B X=A+B A B C X=A+B+C
- 16. FOR THREE INPUT OR GATE INPUT OUTPUT X Y Z O=X+Y+Z 0 0 0 0 0 0 1 1 0 1 0 1 0 1 1 1 1 0 0 1 1 0 1 1 1 1 0 1 1 1 1 1
- 17. THREE INPUT OR GATE USING 2/1 OR GATE
- 18. THE NAND GATE • The NAND gate is the one of the popular logic element because it can be used as a universal gate; that is NAND gate can be used in combination to perform the AND, OR, and inverter operations. • NAND Gate is constructed by attaching NOT Gate at the output of AND Gate, hence NAND Gate is called NOT- AND Gate. • NAND Gate has two or more input and only one output. • The output of NAND gate is low when all inputs are high, otherwise all outputs are high.
- 19. OPERATION OF A NAND GATE • A NAND gate produces a Low output only when all the inputs are High. When any of the inputs is Low, the output will be High. Logical Symbol Inputs Output A B X 0 0 1 0 1 1 1 0 1 1 1 0 Truth Table
- 21. LOGICAL EXPRESSION OF NAND • It’s logical expression is, X= (AB)’ Inputs A B 0 0 (0.0)’= 0’=1 0 1 (0.1)’= 0’=1 1 0 (1.0)’= 0’=1 1 1 (1.1)’= 1’=0
- 22. FOR THREE INPUT NAND GATE INPUT OUTPUT X Y Z O=(X.Y.Z)’ 0 0 0 1 0 0 1 1 0 1 0 1 0 1 1 1 1 0 0 1 1 0 1 1 1 1 0 1 1 1 1 0
- 23. THREE INPUT NAND GATE USING 2/1 NAND GATE
- 24. THE NOR GATE • The NOR gate, like the NAND gate, NOR gate is also useful logical element because it can also be used as a universal gate. • NOR gate can be used in combination to perform the AND, OR and Inverter operations. • NOR Gate is the combination of NOT gate at the output of OR gate, hence NOR gate is type of NOT-OR gate. • NOR gate has two or more input and only one output. • The Output of NOR gate is high when all inputs are low otherwise the output is low.
- 25. OPERATION OF NOR GATE • A NOR gate produces a Low output when any of its inputs is high. Only when all of it’s inputs are low is the output high. Logical Symbol Inputs Output A B X 0 0 1 0 1 0 1 0 0 1 1 0 Truth Table
- 27. EXPRESSION OF NOR GATE • It’s expression is, X=(A+B)’ Inputs A B 0 0 (0+0)’= 0’=1 0 1 (0+1)’= 0’=0 1 0 (1+0)’= 0’=0 1 1 (1+1)’= 1’=0
- 28. FOR THREE INPUT NOR GATE INPUT OUTPUT X Y Z O=(X+Y+Z)’ 0 0 0 1 0 0 1 0 0 1 0 0 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 0 1 1 1 0
- 29. THREE INPUT NOR GATE USING 2/1 NOR GATE
- 30. THE EXCLUSIVE- OR GATE • The exclusive-OR gate has a graphical symbol similar to that of the OR gate, except for the additional curved line on the input side. • It can take only 2 inputs. • We can’t construct Ex-OR Gate using three input Ex-OR gate. • If both inputs are Low or both are High then it produces the output Low or 0. otherwise it produce the High.
- 31. TRUTH TABLE • Logical Symbol Inputs Output A B AB’+A’B=X 0 0 0.0’+0’.0 =0+0=0 0 1 0.1’+0’+1=0+1=1 1 0 1.0’+1’.0=1+0=1 1 1 1.1’+1’.1=0+0=0
- 32. LOGICAL EXPRESSION • It’s logical expression is X=AB’+A’B • 𝑋 = 𝐴 ⊕ 𝐵
- 33. EXCLUSIVE-NOR GATE • The exclusive-NOR gate is the complement of the exclusive-OR gate, as indicated by small circle on the output side of the graphic symbol. • It can take only 2 inputs. • We can’t construct Ex-NOR Gate using three input Ex-OR gate. • If both inputs are Low or both are High then it produces the output High or 1. otherwise it produce the Low output.
- 34. TRUTH TABLE • Logical symbol Inputs Output A B AB’+A’B=X 0 0 0.0+0’.0’=0+1=0 0 1 0.1+0’+1’=0+0=0 1 0 1.0+1’.0’=0+0=0 1 1 1.1+1’.1’=1+0=1
- 35. LOGICAL EXPRESSION • It’s logical expression is 𝑋 = 𝐴𝐵 + 𝐴′ 𝐵′ • 𝑋 = 𝐴 ⊙ 𝐵