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CommendableColumbus7391

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digital logic circuits logic gates boolean algebra digital electronics

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This document is a digital lecture, textbook, or study guide on digital logic circuits. It covers various topics such as logic gates, their operations, and truth tables, including those for OR, AND, NOT, NAND, NOR, and XOR/EX-OR gates. It also demonstrates how these logic functions can be combined to build more complex logic circuits.

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Digital Logic Circuits 1 Logic Gates * A logic gate is an electronic circuit which makes logical decisions, the most common logic gates are AND, OR, NOT gates. * The NAND and NOR gates are called as the Universal gates. * The exclusive OR gates is anothe...

Digital Logic Circuits 1 Logic Gates * A logic gate is an electronic circuit which makes logical decisions, the most common logic gates are AND, OR, NOT gates. * The NAND and NOR gates are called as the Universal gates. * The exclusive OR gates is another logic gate which can be constructed using basic gates such as AND, OR, NOT. * There are more type of logic gates. 2 Logic Gates : * OR Gate. * AND Gate. * NOT Gate. * NAND Gate. * NOR Gate. * Exclusive-OR(Ex-OR) Gate. 3 OR Gate : * The OR gate performs Logic addition, it is known as OR function. * The OR gate has two or more inputs and only one output. Y = A+B The OR function can be expressed as Y = A+B+C+D+…….. 4 A Y=A+B B a) Logic Symbol Input Output A B Y= A+B 0 0 0 0 1 1 1 0 1 1 1 1 b) OR gate truth table 5 AND Gates : * The AND gate performs logical multiplication, it is known as AND function. * The AND gate has two or more input and a single output. Y= A. B * Where the dot(.) denotes the AND operation. Y =AB 6 A Y=AB B a) Logic Symbol Input Output A B Y= AB 0 0 0 0 1 0 1 0 0 1 1 1 b) AND gate truth table 7 NOT gate : * The NOT gate performs the basic logical function called inversion or complementation. * The purpose of the gate is to convert one logic level into the opposite logic level. Input Output Y= A A Y=A A 0 1 1 0 a) Logic Symbol b) NOT gate truth table 8 NAND gate : * NAND is a contraction of the NOT-AND gates. * It has two or more inputs and only one output. Input Output A A B Y= AB Y=AB 0 0 1 B 0 1 1 1 0 1 1 1 0 a) Logic Symbol b) NAND gate truth table 9 9 NOR gate : * NOR is a contraction of NOT-OR gates. * It has two or more inputs and only one output. Input Output A B Y= A+B A Y=A+B 0 0 1 B 0 1 0 1 0 0 1 1 0 a) Logic Symbol b) NOR gate truth table 10 Exclusive-OR(Ex-OR) gate : * An Exclusive-OR gate is a gate with two or more inputs and one output. * The output of a two-input Ex-OR gate a HIGH state. Input Output A B Y= A +B Y=A + 0 0 0 B 0 1 1 1 0 1 1 1 0 a) Logic Symbol b) Ex-OR gate truth table 11 Boolean Algebra * Boolean Algebra , elements have one of two values –True or False. * The circuits in a computer are also designed for two-state operations. * That is input and output of a circuit is either low(0) or high(1). * The circuits are called logic circuits. 12 Boolean Algebra : There are three basic operators in Boolean Algebra which are called logical operators or Boolean operators. 1. OR - logical addition 2. AND – logical multiplication 3. NOT – Logical negation The Boolean operators are used to combine Boolean variables and Boolean constants to form Boolean Expressions. 13 OR Operation AND Operation 14 NOT Operation DeMorgan’s law : 1. (A.B)’= A’+ B’ 2. (A+B)’= A’. B’ 15 Boolean Algebra The sum-of-products form for our function is: We note that this function is not in simplest terms. Our aim is only to rewrite our function in canonical sum-of-products form. 16 Map Simplification K – Map Simplification : K-map method can also be used for simplifying the logic expression for s and c-out. AB AB C out 00 01 11 10 C out 00 01 11 10 0 0 0 1 0 0 0 1 0 1 1 0 1 1 1 1 1 0 1 0 b) K-map for C out a) K-map for Sum 17 Two variable k-map Three variable B B B 0 1 BC 00 01 A 11 10 A 0 1 0 0 1 3 2 A 1 2 3 4 5 7 6 A 1 Four Variable k-map CD C 00 01 11 10 C AB 00 0 1 3 2 01 4 5 7 6 11 12 13 15 14 B A 10 8 9 11 10 18 Example for k – Map : Product of sum simplification 1 1 0 1 0 1 0 0 0 0 0 0 1 1 0 1 Formula : F’ = AB+CD+BD’ F = (A’+B’)(C’+D’)(B’+D) 19 Combinational Circuits Combinational logic circuits are circuits in which the output at any time depends upon the combination of the input signals. * Multiplexers * De-Multiplexers * Encoders * Decoders 20 Multiplexers (Data Selectors) * The term ‘multiplex’ means “many into one”. Multiplexing is the process of transmitting a large number of information over a single line. * A digital multiplexer is a combinational circuit that selects one digital information from several source and transmits the selected information on a single output line. * A multiplexer is also called a data selector. m select signals n input 1 output signal Multiplexer signal 21 De-multiplexers(Data Distributors) * The “demultiplex” means “one into many”. * Demultiplexing is the process of taking information from one input and transmitting the same over one of several output. * A demultiplexer is a logic circuit the receives information on a single input and transmits the same information over one for several (2n) output lines. m select signals n input Demultiplexer 1 output signal signal 22 Encoders * An encoder is a digital circuit that performs the inverse operation of a decoder and the opposite of the decoding process is called encoding. * Encoder is a combinational logic circuit that convert an active input signal into a coded output signal. m outputs n input Encoders 23 Octal-to-Binary Encoder : It is well-known that a binary-to-octal decoder a 3-bit input code and activates one of eight output lines corresponding to that code. Input Output D0 D1 D2 D3 D4 D5 D6 D7 Y2 Y1 Y0 1 0 0 0 0 0 0 0 0 0 0. 0 1 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 1 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 1 1 1 1 24 Decoders * A decoder is similar to a demultiplexer but operates without any data input. In digital systems, decoding is often essential. Decoding Applications: Decoders are used in data demultiplexing, digital displays, digital-to-analog converters, and memory addressing. Output Activation: Each output line is activated for only one of the possible combinations of input signals. Input-Output Relationship: In a decoder, the number of outputs is greater than the number of inputs, allowing unique binary input combinations to activate specific outputs. 25 3-to-8 Decoder : A 3-to-8 decoder has three input (A,B,C) and eight output(D0 to D7) based on 3 input one of the eight output is selected. Input Output A B C D0 D1 D2 D3 D4 D5 D6 D7 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 0 0 1 0 1 1 1 0 0 0 0 0 0 0 1 26 Flip Flops * The simplest type of sequential circuit is a memory cell known as a flip-flop, which has only two stable states. * It is used to store One bit of information with a 0 or a 1. * A flip flop is also known as bistable, multivibrator, latch or toggle. 27 Type of flip flop : * Flip-flops come in various types, depending on their inputs and how clock pulses trigger transitions between their two stable states. * There are four types of flip flop. * S-R Flip flop (Set/Reset). * D Flip flop (Delay/Data). * J-K Flip flop. * T Flip flop (Toggle). 28 S – R Flip Flop (SET/RESET) 29 30 Working of S – R Flip Flop (Set/Reset) : * If both S and R are 0 during transition, the output does not change. * If S= 1 and R= 0, the out put Q is set to 1. * If S= 0 and R=1, the output is cleared or reset to 0. * If both S and R are 1, the output is unpredictable. This condition makes the RS flip flop difficult to manage and therefore is forbidden in practice. 31 D - Flip Flop (DELAY/DATA) 32 33 Working of D – Flip Flop : The D input goes directly into the S input and the complement of the D input goes to the R input. * If it is 1, the flip-flop is switched to the set state (unless it was already set). * If it is 0, the flip-flop switches to the clear state. Applications: 1. Registers as storage devices. 2. Used as a Buffer. 3. In Digital system. 34 JK - Flip Flop (DELAY/DATA) 35 36 Working of JK – Flip Flop : * When j and k both are 0, the data inputs have no effect on the outputs. * When j=0 and k=1, the flip flop is reset or cleared to 0. * When j=1 and k=0. the flip flop is set to 1. * When j and k are 1, if the state of flip flop was 0,applying a clock with 1and flip flop state was 1, it changes to 0. 37 * This on off state is TOGGLING. * Racing condition: Toggling between 0 to 1 and 1 to 0 alternatively for one clock cycle. Application: 1. Counters. 2. Frequency Dividers. 3. Register. 38 T - Flip Flop (TOGGLE) 39 40 Working for T – Flip Flop : * The T - flip flop is also known as the TOGGLE - flip flop. The toggle mode of JK flip flop is used as T - Flip flop. * This Flip flop can be obtained from a JK flip flop when inputs J and K are connected to provide a single input designated by T. * The T flip-flop is a single input version of the JK flip - flop. The T flip flop is obtained from the JK type if both inputs are tied together. 41 * The output of the T flip-flop "toggles" with each clock pulse. * When t=0, (j=0, k=0) the clock transition does not change. * When t=1, (j=1, k=1) the clock transition complements the state. 42 Sequential Circuit * Sequential Logic circuits remember past inputs and past circuit state. * Outputs from the system are “fed back” as new inputs With gate delay and wire delay * The storage elements are circuits that are capable of storing binary information: memory 43 Sequential Circuits : Circuits that we Information Storing have learned Circuits so far Timed “States” Sequential Circuits Diagram 44 Synchronous Sequential Circuits: Flip flops as state memory The flip-flops receive their inputs from the combinational circuit and also from a clock signal with pulses that occur at fixed intervals of time, as shown in the timing diagram. 45 Thank You 46

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