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COMPUTER ORGANIZATION - Logic gates, Boolean Algebra, Combinational Circuits

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COMPUTER ORGANIZATION - Logic gates, Boolean Algebra, Combinational Circuits

1. 1. COMPUTER ORGANIZATION Logic Gates, Boolean Algebra, Combinational Circuits
2. 2. Logic Gates A logic gate is an elementary building block of a digital circuit. Most logic gates have two input and one output. At any given moment, every terminal is in one of the two binary conditions low (0) or high (1), represented by different voltage levels. There are seven basic logic gates: AND, OR, XOR, NOT, NAND, NOR, and XNOR. 0 is called "false" and 1 is called "true,”
3. 3. AND Gate • The output is "true" when both inputs are "true." Otherwise, the output is "false." Input 1 Input 2 Output 0 0 0 0 1 0 1 0 0 1 1 1
4. 4. OR Gate • The OR gate gets its name from the fact that it behaves after the fashion of the logical inclusive "or." The output is "true" if either or both of the inputs are "true." If both inputs are "false," then the output is "false.“ Input 1 Input 2 Output 0 0 0 0 1 1 1 0 1 1 1 1
5. 5. XOR Gate • The XOR ( exclusive-OR ) gate acts in the same way as the logical "either/or." The output is "true" if either, but not both, of the inputs are "true." The output is "false" if both inputs are "false" or if both inputs are "true." Input 1 Input 2 Output 0 0 0 0 1 1 1 0 1 1 1 0
6. 6. NOT Gate • logical inverter , sometimes called a NOT gate to differentiate it from other types of electronic inverter devices, has only one input. It reverses the logic state. Input Output 1 0 0 1
7. 7. NAND Gate • The NAND gate operates as an AND gate followed by a NOT gate. It acts in the manner of the logical operation "and" followed by negation. The output is "false" if both inputs are "true." Otherwise, the output is "true." Input 1 Input 2 Output 0 0 1 0 1 1 1 0 1 1 1 0
8. 8. NOR Gate • The NOR gate is a combination OR gate followed by an inverter. Its output is "true" if both inputs are "false." Otherwise, the output is "false." Input 1 Input 2 Output 0 0 1 0 1 0 1 0 0 1 1 0
9. 9. XNOR Gate • The XNOR (exclusive-NOR) gate is a combination XOR gate followed by an inverter. Its output is "true" if the inputs are the same, and"false" if the inputs are different Input 1 Input 2 Output 0 0 1 0 1 0 1 0 0 1 1 1
10. 10. • Using combinations of logic gates, complex operations can be performed. In theory, there is no limit to the number of gates that can be arrayed together in a single device. • But in practice, there is a limit to the number of gates that can be packed into a given physical space. • Arrays of logic gates are found in digital integrated circuits (ICs). • As IC technology advances, the required physical volume for each individual logic gate decreases and digital devices of the same or smaller size become capable of performing ever-more-complicated operations at ever- increasing speeds.
11. 11. Boolean Algebra • A set of rules formulated by the English mathematician George Boole describe certain propositions whose outcome would be either true or false. • With regard to digital logic, these rules are used to describe circuits whose state can be either, 1 (true) or 0 (false). • In order to fully understand this, the relation between the an AND gate, OR gate and NOT gate operations should be appreciated. • A number of rules can be derived from these relations as shown in the below table.
12. 12. Boolean Laws
13. 13. Using the truth table: • Example 1 solving algebraically
14. 14. Example 2 Example 3
15. 15. Combinational Circuits • Combinational circuit is circuit in which we combine the different gates in the circuit for example encoder, decoder, multiplexer and demultiplexer. Some of the characteristics of combinational circuits are following. • The output of combinational circuit at any instant of time, depends only on the levels present at input terminals. • The combinational circuit do not use any memory. • The previous state of input does not have any effect on the present state of the circuit. • A combinational circuit can have a n number of inputs and m number of outputs.
16. 16. Block Diagram
17. 17. • Half Adder • Half adder is a combinational logic circuit with two input and two output. • The half adder circuit is designed to add two single bit binary number A and B. • It is the basic building block for addition of two single bit numbers. • This circuit has two outputs carry and sum.