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11. Fundamentals of Digital Electronics - Logic Gates.pptx

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IJERA Journal

Logic gates are the fundamental components of any digital system and can be considered the "building blocks". A logic gate is a simple electric circuit consisting of two inputs and a single output. The most frequent names for logic gates are AND, OR, NOT, XOR (Exclusive or), NAND (NOT AND), and NOR. An OR logic gate begins with the provision of two electrical inputs. If one of the inputs has the value one or indicates that it is "on," then the output will also be one. In electronics, there is a type of logic gate known as an inverter or NOT gate. The report is broken up into five distinct parts or sections. The first section of this report covers the experiment's results on logic gates. They are used in the process of performing logical operations on one or more binary inputs to produce a single binary output. This article will examine the functions of the NOT, OR, and AND gates found in a logic circuit. The findings of the experiment are presented in the fourth section. The discussion, recommendations, and conclusions drawn from the results are in the last part. In a NOT gate, the input determines whether the output is true or false, and vice versa. ALTERNATIVELY, gates output a value of HIGH if either of the two inputs is. HIGH and LOW if both inputs are LOW; this type of gate is also known as an inverter. A truth table was used to validate the information of each NOT, AND, and OR integrated circuit. Knowing how to use these seven fundamental logic gates makes it much simpler to comprehend Boolean algebra and simplifies the process of conducting circuit analysis. These gates are most commonly used in the manufacture of automatic machines. Learning how to design logical circuits was made possible by utilizing gates such as NOT, AND, and OR.

Abdualrahman Kdh

Journal of Computer Sciences and Applications

sciepub.com SciEP

Rules and laws of Boolean algebra are very essential for the simplification of a long and complex logic equation. Applying the Boolean algebra basic concept, such a kind of logic equation could be simplified in a more simple and efficient form.Mainly, the standard rules of Boolean algebra are given in operator ‘+’ and ‘x’, based on the AND and OR logic gates equations. For some logic designs, it is commonly that logic problems are writtenin terms of XOR format.This paper tries to conduct something different. It will analyze, describe, and derive Boolean algebra rules related to logic equations using exclusive-or (XOR) logic gate.

Abstract: In this Paper we have discussed different types of logic gates (AND,OR,NOT,NAND,NOR,XOR,XNOR) and corresponding logic tables. The base of any digital computer system are logic gates or circuits which performs logical operations on chunks of information represented digitally. Logic gates work on the basis of binary digits 0 and 1.Any intelligent system with the abilities to take decision comprises of simple logic gates. This paper is an attempt to bring forth the application of digital logic gates in day to day life with some real time applications as well like burglar alarm and security system. Through the study of no. of physical sytems e.g. mechanical, optical, electrical, thermal, biological systems it can be said that modeling of any such system can be done logically with the help of a Boolean expression. Accordingly such a system can be studied mathematically. This paper is a generic effort in understanding the Boolean mathematics behind the physical system around.

John Pradeeb

Y = A ⊕ B = A B + AB H = HIGH Logic Level L = LOW Logic Level

muhammed nishad

Variable, complement, and literal are terms used in Boolean algebra. A variable is a symbol used to represent a logical quantity. Any single variable can have a 1 or a 0 value. The complement is the inverse of a variable and is indicated by a bar over variable (overbar). For example, the complement of the variable A is A. If A = 1, then A = 0. If A = 0, then A = 1. The complement of the variable A is read as "not A" or "A bar." Sometimes a prime symbol rather than an overbar is used to denote the complement of a variable; for example, B' indicates the complement of B. A literal is a variable or the complement of a variable. Boolean Addition Recall from part 3 that Boolean addition is equivalent to the OR operation. In Boolean algebra, a sum term is a sum of literals. In logic circuits, a sum term is produced by an OR operation with no AND operations involved. Some examples of sum terms are A + B, A + B, A + B + C, and A + B + C + D. A sum term is equal to 1 when one or more of the literals in the term are 1. A sum term is equal to 0 only if each of the literals is 0. Example Determine the values of A, B, C, and D that make the sum term A + B + C + D equal to 0.

Panca Kurniawan

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Introduction to Logic Gates

Published by Utami Budiono Modified over 4 years ago

Presentation on theme: "Introduction to Logic Gates"— Presentation transcript:

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Logic Gates Combinational Circuits

Nov 05, 2014

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Logic Gates Combinational Circuits. Logic Gates. A logic gate is an elementary building block of a digital circuit. Most logic gates have two input and one output.

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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,”

AND Gate • The output is "true" when both inputs are "true." Otherwise, the output is "false."

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.“

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."

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.

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."

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."

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

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.

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.

Block Diagram

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.

Full adder is developed to overcome the drawback of Half Adder circuit. It can add two one-bit numbers A and B, and carry c. The full adder is a three input and two output combinational circuit.

N-Bit Parallel Adder • The Full Adder is capable of adding only two single digit binary number along with a carry input. • But in practical we need to add binary numbers which are much longer than just one bit. • To add two n-bit binary numbers we need to use the n-bit parallel adder. • It uses a number of full adders in cascade. • The carry output of the previous full adder is connected to carry input of the next full adder.

4 Bit Parallel Adder • In the block diagram, A0 and B0 represent the LSB of the four bit words A and B. Hence Full Adder-0 is the lowest stage. • Hence its Cin has been permanently made 0. The rest of the connections are exactly same as those of n-bit parallel adder is shown in fig. • The four bit parallel adder is a very common logic circuit.

Half Subtractors • Half subtractor is a combination circuit with two inputs and two outputs (difference and borrow). • It produces the difference between the two binary bits at the input and also produces a output (Borrow) to indicate if a 1 has been borrowed. • In the subtraction (A-B), A is called as Minuendbit and B is called as Subtrahend bit. • Corrections to be done in images

Full Subtractors • The full subtractor is a combinational circuit with three inputs A,B,C and two output D and C'. • A is the minuend, B is subtrahend, C is the borrow produced by the previous stage, D is the difference output and C' is the borrow output. • The disadvantage of half subtractor about not considering the borrow of previous stage is overcome by full subtractor.

Full Subtractors

N-Bit Parallel Subtractor • The subtraction can be carried out by taking the 1's or 2's complement of the number to be subtracted. • For example we can perform the subtraction (A-B) by adding either 1's or 2's complement of B to A. • That means we can use a binary adder to perform the binary subtraction.

4 Bit Parallel Subtractor • The number to be subtracted (B) is first passed through inverters to obtain its 1's complement • The 4-bit adder then adds A and 2's complement of B to produce the subtraction. • S3 S2 S1 S0 represent the result of binary subtraction (A-B) and carry output Cout represents the polarity of the result. • If A > B then Cout =0 and the result is in the binary form (A-B) AND • if A<B then Cout = 1 and the result is in the 2's complement form.

4 Bit Parallel SUBTRACTOR

Multiplexers • It has n-data inputs, one output and m select inputs with 2m = n & is called n:1 multiplexer • It is a digital circuit which selects one of the n data inputs and routes it to the output. • Depending on the digital code applied at the selected inputs, one out of n data sources is selected and transmitted to the single output Y. • E is called the strobe or enable input which is useful for the cascading and will perform the required operation only when it is low. • For 10 data inputs to be multiplexed no. of select lines and type of multiplexer required will be……..

Multiplexers A 2:1 multiplexer block diagram and realization

Demultiplexers • A demultiplexer performs the reverse operation of a multiplexer i.e. it receives one input and distributes it over one of the outputs. • It has only one input, n outputs, m select input. At a time only one output line is selected by the select lines and the input is transmitted to the selected output line. • Always 2m>n for a 1:n demultiplexer

Demultiplexers A 2:1 demultiplexer block diagram and truth table

Decoder • A decoder is a combinational circuit having n input and to a maximum m = 2n outputs. • i.em (output count) > n (input count) • Decoder is identical to a demultiplexer without any data input where select lines behave as a n inputs. • It performs operations which are exactly opposite to those of an encoder.

2 to 4 Line Decoder • A and B are the two inputs where D through D are the four outputs. • From Truth table it appears that each output is 1 for only a specific combination of inputs & all other outputs being zero

2 to 4 Line Decoder Logic circuit

Encoder • It performs the inverse operation of the decoder • An encoder has n number of input lines and m number of output lines. ( • An encoder produces an m bit binary code corresponding to the digital input number. • The encoder accepts an n input digital word and converts it into an m bit another digital word • Examples of Encoders are following. • Priority encoders • Decimal to BCD encoder • Octal to binary encoder • Hexadecimal to binary encoder

Priority Encoder • Here priority is given to the input lines. • If two or more input lines are 1 at the same time, then the input line with highest priority will be considered. • There are four input D0, D1, D2, D3 and two output Y0, Y1. • Out of the four input D3 has the highest priority and D0 has the lowest priority. • That means if D3 = 1 then Y1 Y0 = 11 irrespective of the other inputs. Similarly if D3 = 0 and D2= 1 then Y1 Y0 = 10 irrespective of the other inputs.

Priority Encoder

Priority Encoder Y1= D3 + D2 Y0 = D3 + D1 ! D2

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LOGIC GATES - EXOR • The 'Exclusive-OR' gate is a circuit which will give a high output if either, but not both, of its two inputs are high. An encircled plus sign ( ) is used to show the EOR operation. Activity: Draw a circuit that shows how the EXOR gate would be drawn using ONLY the basic logic gates.
PDF Logic gates
logic symbol The output should be low when both of the two inputs are high, so the nMOS transistors are in series. The output should be high when either of the two inputs are low, so the pMOS transistors (which are on when the corresponding input is low) are in parallel. This produces the following CMOS implementation. V DD V DD output A B ...
PPT
Introduction to Logic Gates. Nov 16, 2014. 570 likes | 1.22k Views. Introduction to Logic Gates. Logic Gates The Inverter The AND Gate The OR Gate The NAND Gate The NOR Gate The XOR Gate The XNOR Gate Drawing Logic Circuit Analysing Logic Circuit. Introduction to Logic Gates. Universal Gates: NAND and NOR NAND Gate NOR Gate. Download Presentation.
PDF Boolean Algebra & Logic Gates
Boolean Algebra - Postulates. An algebraic structure defined by a set of elements, B, together with two binary operators + and . that satisfy the following postulates: Postulate 1: Closure with respect to both (.) and ( +) Postulate 2: An identity element with respect to +, designated by 0. An identity element with respect to . designated by 1.
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Logic Gates - Boston University ... Logic Gates
11. Fundamentals of Digital Electronics
Logic gates work on the basis of binary digits 0 and 1.Any intelligent system with the abilities to take decision comprises of simple logic gates. This paper is an attempt to bring forth the application of digital logic gates in day to day life with some real time applications as well like burglar alarm and security system. Through the study of ...
Simple logic gates (2.1.11-2.1.13)
SIMPLE LOGIC GATES. 2.1.11 Define the Boolean operators: AND, OR, NOT, NAND, NOR and XOR. In computer science, the Boolean data type is a data type that has one of two possible values (usually denoted true and false), intended to represent the two truth values of logic and Boolean algebra. It is named after George Boole, who first defined an ...
Introduction to Logic Gates
Download ppt "Introduction to Logic Gates". What are Logic Gates? Description …. Basic building blocks of a digital circuit Data processing on the circuit is controlled using transistors Output depends on the logic gate and the input Input is one of two states - high or low Output is one of two states - high or low There are seven types ...
PDF Logic Design Lecr 02 Logic Gates.ppt
The AND Gate for more than 2 inputs. The OR gate produces a HIGH output if any input is HIGH; if all inputs are LOW, the output is LOW. For a 2-input gate, the truth table is. The OR operation is shown with a plus sign (+) between the variables. Thus, the OR operation is written as X = A + B. Example waveforms:
Presentation On Logic Gates
NOT Gate Truth Table Symbol 1 Inverter or NOT Gate Boolean Expression Q = not A or A Truth Table Q 1 0 1 Read as inverse of A gives Q. NOT equivalent NAND and NOR Gate Equivalents An Inverter or logic NOT gate can also be made using standard NAND and NOR gates by connecting together ALL their inputs to a common input signal for example. 2-input ...
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PPT - Logic Gates PowerPoint Presentation, free download
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Logic Gates Powerpoint
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Presentation Transcript. Digital Electronics Logic Gates Logic gates work with the voltage level of the signals. They are discrete devices that understand only a High voltage level and Low voltage level. For certain digital devices a High is 5 Volts and Low is 0 Volts. Following describes the behavior of three fundamental logic gates in digital ...
Logic Gates And Boolean Algebra
Presentation Transcript. Logic Gates- AND A logic gate has 2 inputs which outputs either ON or OFF (1 or 0). If an off value is in one of the input values for an AND gate, the output will remain off. So an output of 1 can come from an AND gate only if both inputs are on or '1'. Output Q = A AND B.
PPT
Presentation Transcript. Logic Gates Combinational Circuits. 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.