Digital Logic Circuits PDF

Analog System - It is a system that uses continuous values. Digital System - Any system that can be used for the transmission or processing of information in which the information is represented by physical quantities or signals that are so constrained as to take only discrete values. Best known e...

Analog System - It is a system that uses continuous values. Digital System - Any system that can be used for the transmission or processing of information in which the information is represented by physical quantities or signals that are so constrained as to take only discrete values. Best known example of a digital system. Central Processing Unit - the CPU is the Other examples are brains of the computer where most Telephone switching exchange calculations take place. Digital multimeter Digital counters Memory - this stores the program and the Electronic calculators data before the computer run begins Digital displays I/O (Input/Output) - this consists of all the circuits needed to get programs and data in/out of the computer ANALOG VERSUS DIGITAL Control unit - This is the computer's center - Characteristic of a digital system is of gravity, analogous to the conscious part its manipulation of discrete elements of the mind. The control section directs the of information. operation of all other sections. - Such discrete elements may be electric impulses, the decimal digits, Arithmetic Logic Unit - This is the letters of the alphabet, arithmetic number-crunching section of the machine, it operations, punctuation marks, or can also make logical decisions. any other set of meaningful symbols. - The juxtaposition of discrete Register - A group of electronic, magnetic elements of information represents a or mechanical devices that store digital quantity of information. data. NUMBER SYSTEM Digital Computer - an interconnection of Binary Numeral System - represents digital modules. values using two symbols Functional Units of a Computer Octal Numeral System - base of 8 number systems uses the digits 0-7 Decimal Numeral System - has 10 as its base, the numerical base most widely used Hexadecimal Numeral System - base of LOGIC BUFFER GATE: only one input, 16, used in microprocessor and computer output same, and this delays the signal memory address. XOR GATE: high output only when input Base - number of digits in a number system word has odd parity bit XNOR: OR GATE followed by inverter Bit - binary digit, consisting of two states DE MORGAN's THEOREM Nibble - string of 4 bits 1st Theorem: a NOR GATE is equivalent to a bubbled AND gate Byte - string of 8 bits 2nd Theorem: a NAND GATE is equivalent to a bubbled OR gate Binary Code - formed by converting each digit of a decimal number individually into KARNAUGH MAP binary. ASCII (American Standard Code for Sum Term: logical sum of several variables Information Interchange) is the alphanumeric code. Product Term: logical product of several variables STANDARD LOGIC GATES Logic Circuit : input and output signals are Sum of Products(SOP): an AND-OR Ckts two states Karnaugh Map: graphic display of the Gate : one or more input signals, one output fundamental products in the truth table signal Max Term (piM): use only sum terms that Truth Table : shows all input and output contain all the input variables in either possibilities of a logic circuit normal or complemented form OR GATE: 2 or more inputs, one output Minterm/Standard Product(SummationM): represents the AND GATE: output is high when all inputs least combination of the input variables for are high. each output state NOT GATE or INVERTER: 1 input and 1 Adjacent Cells: two cells whose output, output is always the complement of perspective addresses differ by only 1 digit the input Implicant: each product term in the sum of NOR GATE: equivalent of OR GATE product expression followed by inverter Enclosure: denotes an implicant in the NAND GATE: AND GATE followed by karnaugh map inverter Prime Implicant: an implicant that cannot Parallel Adder - allow multiple additions of be enclosed by larger implicant binary digits. A digital circuit that adds two binary numbers in parallel form and BOOLEAN ALGEBRA produces the arithmetic sum of those Boolean Constants - these are ‘0’ (false) numbers in parallel form and ‘1’ (true) Comparator - Used to compare two strings Boolean Variable - can only take the to determine if both are exactly the same. values ‘0’ or ‘1’ Consists of 4 X-NOR gates and 1 AND gate. Boolean Functions - each of the logic functions (such as AND, OR, and NOT) are Magnitude Comparator - capable of represented by symbols as described comparing two binary strings or words if they are equal, greater or less than with Boolean Theorems - set of identities and each other. (available in TTL(IC 7485)) or laws CMOS families. CONSENSUS THEOREM Decoder - multiple-input, multiple-output - Very useful in simplifying boolean logic circuit arranged in manner so as to expressions. XY + X’Z + YZ can be transform coded inputs to coded outputs. written as XY + X’Z Breakdowns any combination of inputs to a set of terms that are all set to '0' apart from Combinational Circuits - when one term. Used in security alarm systems combinational logic, (a logical entity), is and many applications. converted to physical entity. Consists of input variables, cascaded logic gates and N-to-m line Decoders - converts binary output variables. inputs of 'n' into a coded output with a maximum of 2^n different output lines. Half Adder - produces a carry out but cannot accept a carry in. 2-to-4 Decoder - accepts two input (A and B) combinations to produce four (output 1, Full adder - performs addition of three 2, 3, 4) logic outputs. Consists of 4 2-input binary digits. AND gates and 2 NOT gates. Main difference between the two is the carry 3-to-8 line Decoder - used to decode all in process capability of the latter. possible combinations of three input bits. Has three inputs and eight outputs and that Half Subtractor - performs subtraction of is why it is called a 3-bit binary decoder. two binary digits. Consists of 8 AND gates, 12 NOT gates, 3 input lines, 8 output lines. Full Subtractor - subtraction of three bits. Consisting of a minuend, subtrahend, BCD-to-Seven Segment Decoder - borrow in, output difference, and borrow out. convert a BCD input combination into a form which will drive a 7-segment display. Consists of 10 AND gates, 25 NOT gates, 4 convert decimal (10 digits) input into its input lines, 10 output lines. corresponding BCD output. 10 inputs and 4 outputs. Common Anode Decoder - used to drive a common anode 7-segment. ICs Applications of Encoder 4510 74LS47 1. Computer Keyboard - uses encoders to minimize the number of wire needed in the Common Cathode Decoder - drives a circuit common cathode 7-segment. IC's 74LS48 2. Computer Hardware Detection System - and 4511 uses an encoder for the CPU to detect which I/O device has requested for Both of these decoders are not communication. interchangeable. 3. Positional Encoders - used in magnetic positional control that guides the ships and 7-Segment Display - provides a robots (mobile) in determining locations. convenient way of displaying information or digital data in the form of numbers, letters or Multiplexer - used for combining several alpha-numeric characters using 7 digits signals into an aggregate bit stream, connected LEDs, placed together on a simply a data selector. single display package. - Also called "Mux" or "Muxes" and works like a rotary switch that connects multiple Memory Address Decoder - used to input lines (2, 4, 8, 16, etc.) into a single control the access and use of a memory unit common output line. in a modern microprocessor system. 2-to-1 line Multiplexer - a circuit that Encoder - device that accepts all the data consists of two input lines with one output inputs at a time and converts this data into a line. single encoded output. 4-to-1 line multiplexer - a circuit that 4-to-2 Line Decoder - single bit encoder consists of four input lines with one output that has 4 bits input and 2 bits output. line. Consists of 1 AND gate, 1 OR gate, and 2 NOT gates. 8-to-1 line multiplexer - consists of eight input lines with one output line. Consists of Priority Encoder - prioritizes a number of 4 input NAND gates, one 8-input NAND significant input bits in the data stream, and gate and 4 NOT gates. once it detects a high input, it will ignore the other bits. Every m inputs are designated Demultiplexer - performs the opposite with its own priority. The Most Significant Bit function of a multiplexer. Accepts a single (MSB): highest priority, Least Significant Bit input data to produce 2^n output lines. (LSB): Lowest priority. converts a serial data signal at the input into a parallel data output. Can also 10-to-4 Line Decoder - also known as function as a decoder by using address Decimal-to-BCD encoder, a circuit used to inputs as binary inputs and providing an output that matches the address input. 1-to-2 line demultiplexer - a circuit with one input line and two output lines. Transfers data from a single input to the selected output. 1-to-4 line demultiplexer - circuit with one input line and four output lines. Also has two data select inputs that determine the outputs. Consists of 4 AND gates and 4 NOT gates 1-to-8 line demultiplexer - one input line and eight output lines. Three data select inputs that determine the outputs. Consists 2. D Latch - also known as Data latch. of 8 AND gates and 3 NOT gates. Very useful variation of the SR latch. The D latch circuit removes one of the inputs by driving both set and Latch - has two stable states and is reset with a complementary capable of storing one bit of information. driver. Latches are considered asynchronous circuits. Types of Latch 1. SR Latch - considered the most basic latch circuit available where S stands for Set and R for Reset. Cross-coupling with two NOR gates and its store bit is available on its output (Q) 3. JK Latch - simple enhancement of the SR latch that removes the indefinite state (S=1, R=1) of the latch by toggling the outputs (Q and Q’) when both input is equal to 1.  Flip-flop - a synchronous bistable circuit. Synchronous because the output changes only when the clock input is active or triggered. It is the common element used as a storage element for computers and other devices. Shown above is a clock signal represented by a square wave that rises and falls. Determines the switching from 0 to 1 at constant intervals. 4. T Latch - formed by shortening the two inputs of JK latch. T latch also known as “Toggle” latch provides a toggle output of the input if the enable line is high. Shown above is the basic feedback logic circuit. Has a NOT gate whose output is connected (shorted) to its own input. Comparison between Latch and Flip Flop 1. Latches are asynchronous; output varies after the change in input. Flip Flops are synchronous; variation of the output state does not only depend on the input but also to a supplied clock pulse. 2. Latches are level sensitive (only 0 and 1 level), as shown in the circuit below. When the enabled input is 1, the input state of the SR is not recognized. When enable is high; inputs of S and R are processed into a sequential circuit. Flip Flops Flip-flops are edge sensitive (depends on the rising and falling of the clock edge). They're used to store information 3. JK Flip Flop - a JK Latch with clock in computers. Uses a SR flip-flop. This input and is considered the most flip-flop has two parts, and they work versatile flip flop because it gives together to store information. When the a definite output if both inputs are clock signal changes, it triggers the 1. flip-flop to change its state. This is called an edge-triggered flip-flop. 3. Both latch and flip-flop have the same circuit design. Only differences in that latch; enable line is replaced by a clock input. Types of Flip Flops 1. SR Flip Flop - SR latch with a clock input. 4. T Flip Flop - changes its output on each clock edge. A simplified version of the JK flip-flop and is commonly used in constructing different types of counters. 2. D Flip Flop - D latch with a clock input. Tracks the input and makes a transition that matches the input. D stands for Data. MASTER AND SAVE FLIP FLOPS Master and Slave Flip Flop - second class flip flop is the master-slave flip flops. Constructed using two separate flip-flops. Edge triggered; the data is entered in the circuit during the leading edge of the clock pulse. 4. Master Slave T Flip Flop - consists of two T Flip Flops connected in series sharing the same clock pulse input. 1. Master-Slave SR Flip Flop - edge sensitive device consisting of two identical clocked SR Flip flops cascaded with each other. Multivibrators An electronic circuit that is capable of providing two state systems. Used to control signal pulses and commonly used in flip flops, clock generators and oscillators. Basically an oscillator that generates a rectangular or square wave. 2. Master Slave D Flip Flop - consists of two D Flip Flops with a NOT gate Types of Multivibrator connected to the slave flip flop’s 1. Astable Multivibrator - no stable clock enable. It is also known as state. A circuit that produces an “Delay Line” because it delays the output that is unstable in either state. operation, whatever is the input it Oscillation of the output continuously is also the output. varies from one state to another. It is also called “Free-Running Multivibrator” because of its free use and continuously once the circuit is turned ON. 3. Master-Slave JK Flip Flop - consists of two JK Flip Flops connected in series sharing the same clock pulse input.  3. Bistable Multivibrator - has two stable states. Trigger provides the circuit with the correct polarity and amplitude causing the output to change state and stay until triggered again. This type of circuit is used as the basic circuit design in developing a register and memory devices. Also called a Flip Flop 2. Monostable Multivibrator - a circuit with one stable state and one unstable state. This type of circuit is ideal for creating timing devices for fixed duration in response to some external event such as a pulse generator, time delay and frequency divider. Registers - Flip flop is 1 bit memory cell Shown below is a one-shot / monostable multivibrator device. Has an input trigger - A register is one or more flip flops that controls the changing of the state, once used to store data. it is set to stable it will stay for a fixed period of time. This is known as the “pulse width”. Shift Register - a sequential logic circuit that consists of a group of flip flops connected in a chain so that the output from one flip flop is the input of the next one on every clock pulse. Below is the circuit diagram of a 4-bit Serial-in Parallel-out register. Types of Synchronous Counters 1. Binary Up Counter - a synchronous that performs counting from 0 to 2^N-1, where N is the number of bits in a given counter circuit. 2. Binary Down Counter - synchronous that performs a down counting from 2^N-1 to 0, N; number of bits.  6. Ring Counter - uses a shift register 3. BinaryUp/Down Counter - circularly connected in series with synchronous counter that follows the only one flip flop being set at any binary number sequence either particular time while the others are going up or down. cleared. 4. Skipping Counter - also known as MOD-N/Divide by N counter. 7. Johnson Counter - Also known as Capable of skipping states that are “Twisted Ring Counter” because the normally part of the counting inverse output of the most significant sequence. flip flop is connected back to the input of the least significant. BILATERAL SWITCH An analog switch consisting of a 5. BCD Counter (Binary Coded gate-controlled MOSFET transistors acting Decimal Counter) - a counter as a switch for analog or digital signal. capable of counting in binary form Works like an ordinary relay switch with from 0000 to 1001 and back. no moving parts in it. CMOS Bilateral Switch behaves like a simple SPST switch controlled electronically, called bilateral because either terminal can be used as an input; to control the movement of each current flows in both directions. switch. Switch option is either A-C or B-C. Single Pole Bilateral Switch - works by connecting together a N-channel and P-channel MOSFET in parallel. This design permits signals to pass through in both directions (bidirectional) one at a time. Read Only Memory Semiconductor Memory - A device that is used to store and retrieve digital data that is fabricated by using integrated circuit technology. - Also called “memory chip” or Types of Bilateral Switches “integrated memory” which is commonly 1. Single Pole Single Throw Switch - used as computer memory. consists of a switch and a non - Used to program and data during inverting amplifier that controls the computer operation and replaces the core movement of the pole. Switch option memory as the main active memory used by is either OFF or A-B. computers. Shown above is the different internal computer memory which is also called semiconductor memory. 2. Single Pole Double Throw Switch - consists of two switches and an Classification of Semiconductor Memory inverting and non-inverting amplifier Random Access Memory(RAM) - volatile Erasable Programmable ROM (EPROM) - (electrically dependent) where data is special type of PROM in which data stored stored temporarily. can be erased using UV light. - Requires constant supply of power to retain data and once power goes off; data will be erased. Read Only Memory (ROM) is an integrated circuit programmed and loaded with specific data when manufactured. ROM chips are commonly used in computers and are non-volatile; not electrically dependent when used. Types of ROM Electrically Erasable Programmable ROM Mask ROM - content is programmed and (EEPROM) - stored data can be erased loaded by the IC manufacturer. Called by exposing it to an electrical charge. “Mask” because of the process ROM is Applying a high voltage(about 21 volts), manufactured. Mask refers to the region single byte of memory are erased in 10ms. of the IC that is masked off before the process of lithography (etching). Programmable ROM (PROM) - permanent memory in which data can be written only one. Commonly used in digital Flash ROM - type of EEPROM that can be appliances and devices such as digital erased and programmed in blocks and washing machines, televisions, digital not by one byte at a time. Enables modern players, playstation, and other digital manufacturers to develop storage device devices. chips that can handle bigger capacity with less circuit requirements, like a flash drive. BIOS uses flash-ROM memory. BIOS contains the driver of the basic I/O devices of the PC/  memory module. Either 30 or 72 pins. 2. Dual In-line Memory Module (DIMM) - two sides of the memory module consists of 168 pins (commonly used although there are others such as 72, 100, 144, and 184 pin) and has a 64 bit connection to other computer hardware. 3. Rambus In-Line Memory Module (RIMM) - developed by Rambus inc that consists of 184 or 232 pins. Commonly used during the Pentium Random Access Memory 3 and early Pentium 4 design Types of RAM computers. 1. Static RAM (SRAM) - uses flip flops 4. Rambus Dynamic RAM (RDRAM) - as a basic storage element. operates at a very high speed of 100 MHZ and transfer data rate of 800 > Cache Memory - a memory bank that MHZ. Consists of 184 pins and bridges the main memory and the used during the same time as RIMM. microprocessor. Data is transferred from 5. Dual Data Ram - capable to the main memory to the cache in blocks. operate at 333 MHz, consists of Using an algorithm there is a greater 284 pins, uses 2.5 volts chance that the next required data is Non Volatile RAM (NVRAM) - retains its already in the cache, resulting in faster content even when the power is turned performance. “An Intelligent memory” OFF. works in contrast with the DRAM and DDR which both require continuous power supply in order to store their data. NVRAM is also known as “Universal Memory” because it has the good characteristics of both RAM and ROM. Video RAM (VRAM) - used in video adapter or 3D graphic accelerator to store images. VRAM works just like a 2. Dynamic RAM (DRAM) - requires a buffer between the processor and the refreshing circuitry to store data. display. Uses a capacitor to store bits of data. Much Slower compared to - Also called a Multiport Dynamic static RAM. Random Access Memory (MPDRAM) because it has two Types of DRAM independent access ports to the 1. Single in-line Memory Module ram, one for the CPU and the other (SIMM) - uses only one side of the for the graphic processor.