Signaler

kavitha muneeshwaranSuivre

1 Feb 2018•0 j'aime## 14 j'aime

•8,886 vues## vues

Soyez le premier à aimer ceci

afficher plus

Nombre de vues

0

Sur Slideshare

0

À partir des intégrations

0

Nombre d'intégrations

0

1 Feb 2018•0 j'aime## 14 j'aime

•8,886 vues## vues

Soyez le premier à aimer ceci

afficher plus

Nombre de vues

0

Sur Slideshare

0

À partir des intégrations

0

Nombre d'intégrations

0

Télécharger pour lire hors ligne

Signaler

Formation

about digital logic circuit in DP&CO

kavitha muneeshwaranSuivre

- Digital Principles and Computer Organization Unit – II Digital Logic Circuits Submitted by, M. Kavitha, M. Sc(CS&IT), Nadar Saraswathi College of Arts and Science, Theni. 1
- Digital Principle and Computer Organization Contents : 1. Logic Gates. 2. Boolean Algebra 3. Map Simplification. 4. Combinational Circuit. 5. Flip Flop. 6. Sequential Circuit. 2
- 3 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.
- 4 Logic Gates : * OR Gate. * AND Gate. * NOT Gate. * NAND Gate. * NOR Gate. * Exclusive-OR(Ex-OR) Gate.
- 5 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+……..
- 6 A B Y=A+B Input Output Y= A+B A B 0 0 0 0 1 1 1 0 1 1 1 1 a) Logic Symbol b) OR gate truth table
- 7 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
- 8 A B Y=AB Input Output Y= AB A B 0 0 0 0 1 0 1 0 0 1 1 1 a) Logic Symbol b) AND gate truth table
- 9 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 A Output Y = A 0 1 1 0 Y= A A a) Logic Symbol b) NOT gate truth table
- 10 NAND gate : * NAND is a contraction of the NOT-AND gates. * It has two or more inputs and only one output. 10 Input Output Y= AB A B 0 0 1 0 1 1 1 0 1 1 1 0a) Logic Symbol b) NAND gate truth table A B Y=AB
- 11 NOR gate : * NOR is a contraction of NOT-OR gates. * It has two or more inputs and only one output. A B Y=A+B Input Output Y= A+B A B 0 0 1 0 1 0 1 0 0 1 1 0a) Logic Symbol b) NOR gate truth table
- 12 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. Y=A B Input Output Y= A B A B 0 0 0 0 1 1 1 0 1 1 1 0a) Logic Symbol b) Ex-OR gate truth table + +
- 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. 13
- 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. 14
- 15 OR Operation AND Operation
- 16 NOT Operation DeMorgan’s law : 1. (A.B)’= A’+ B’ 2. (A+B)’= A’. B’
- 17 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.
- 18 Map Simplification K – Map Simplification : K-map method can also be used for simplifying the logic expression for s and c- out. 0 1 0 1 1 0 1 0 0 0 1 0 0 1 1 1 AB AB C out C out 00 01 11 10 00 01 11 10 0 1 0 1 a) K-map for Sum b) K-map for C out
- 19 0 1 2 3 A B 0 B 1A 1 Two variable k-map Three variable 0 1 3 2 4 5 7 6 A BC 00 01 11 10 0 1 B A C Four Variable k-map 0 1 3 2 4 5 7 6 12 13 15 14 8 9 11 10 AB CD 00 01 11 10 00 01 11 10 A B C
- Example for k – Map : Product of sum simplification Formula : F’ = AB+CD+BD’ F = (A’+B’)(C’+D’)(B’+D) 20 1 1 0 1 0 1 0 0 0 0 0 0 1 1 0 1
- 21 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
- 22 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. Multiplexer 1 output signal m select signals n input signal
- 23 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. Demultiplexer 1 output signal m select signals n input signal
- 24 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. Encoders m outputs n input
- 25 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
- 26 * An decoder is similar to demultiplexer but without any data input. It is most digital systems require the decoding of data. * Decoding is necessary in applications such as data demultiplexing, digital display, digital-to- analog converters and memory addressing. * Each output line will be activated for only one of the possible combinations of inputs. * A decoder is a number of output is greater than the number of inputs. Decoders
- 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. 27 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
- Flip Flops * The simplest kind of sequential circuit is a memory cell that has only two states it is called flip flop. * 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. 28
- 29 Type of flip flop : * Flip flop are of different types depending on the input and clock pulses cause transition between two states. * There are four type of flip flop. * S-R Flip flop (Set/Reset). * D Flip flop (Delay/Data). * J-K Flip flop. * T Flip flop (Toggle).
- S – R Flip Flop (SET/RESET) 30
- 31
- 32 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.
- D - Flip Flop (DELAY/DATA) 33
- 34
- 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. 35
- JK - Flip Flop (DELAY/DATA) 36
- 37
- 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. 38
- * 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. 39
- T - Flip Flop (TOGGLE) 40
- 41
- 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. 42
- * 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. 43
- 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 44
- Sequential Circuits : 45 Sequential Circuits Diagram Circuits that we have learned so far Information Storing Circuits Timed “States”
- 46 Synchronous Sequential Circuits: Flip flops as state memory The flip-flops receive their inputs from theThe flip-flops receive their inputs from the combinational circuit and also from a clock signalcombinational circuit and also from a clock signal with pulses that occur at fixed intervals of time, aswith pulses that occur at fixed intervals of time, as shown in the timing diagram.shown in the timing diagram.
- Thank You 47