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Digital Fundamentals Tenth Edition Floyd Chapter 1 Digital concepts Floyd, Digital Fundamentals, 10th ed 2008 Pearson Education © 2009 Pearson Education,©Upper Saddle River, NJ 07458. All Rights Reserved Summary Digital and Analog Quantities Analog quantity is one having continuous values. Digital quantity is one having a discrete set of values. Floyd, Digital Fundamentals, 10th ed © 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved Summary Digital and Analog Quantities Most natural quantities that we see are analog and vary continuously (For example Air Temperature). Analog systems can generally handle higher power than digital systems. ° Temperature ( F) 100 95 90 85 80 75 70 Time of day 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 A .M . P.M . Digital systems can process, store, and transmit data more efficiently but can only assign discrete values to each point. Floyd, Digital Fundamentals, 10th ed © 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved Summary Digital and Analog Quantities Floyd, Digital Fundamentals, 10th ed © 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved Summary Analog and Digital Systems Many systems use a mix of analog and digital electronics to take advantage of each technology. A typical CD player accepts digital data from the CD drive and converts it to an analog signal for amplification. CD drive 10110011101 Digital data Digital-to-analog converter Linear amplifier Analog reproduction of music audio signal Speaker Sound waves Floyd, Digital Fundamentals, 10th ed © 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved Summary Binary Digits and Logic Levels Digital electronics uses circuits that have two states, which are represented by two different voltage levels called HIGH and LOW. The voltages represent numbers in the binary system. VH(max) In binary, a single number is called a bit (for binary digit). A bit can have the value of either a 0 or a 1, depending on if the voltage is HIGH or LOW. HIGH VH(min) Invalid VL(max) LOW VL(min) Floyd, Digital Fundamentals, 10th ed © 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved Summary Digital Waveforms Digital waveforms change between the LOW and HIGH levels. A positive-going pulse is one that goes from a normally LOW logic level to a HIGH level and then back to its LOW level . A Negative-going pulse generated when the voltage goes from its normally HIGH level to its LOW level and back to its HIGH level HIGH HIGH Rising or leading edge LOW Falling or trailing edge t0 (a) Positive–going pulse t1 Falling or leading edge LOW Rising or trailing edge t0 t1 (b) Negative–going pulse Digital waveforms are made up of a series of pulses. Floyd, Digital Fundamentals, 10th ed © 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved Summary Pulse Definitions -Pulse has two edges: -Leading edge Occurs first at time t0 -Trailing edge Occurs last at time t1 -for a positive-going pulse the leading edge is a rising edge and Trailing edge is a falling edge -Pulses ideal when the rising and falling edges are assumed to change in zero time (in-stantaneously) HIGH HIGH Rising or leading edge LOW Falling or trailing edge t0 (a) Positive–going pulse Floyd, Digital Fundamentals, 10th ed t1 Falling or leading edge LOW Rising or trailing edge t0 t1 (b) Negative–going pulse © 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved Summary Pulse Definitions -Rise time (tr) the time required for a pulse to go from its low level to its high level. -Fall time (tf) the time required for a pulse to go from its high level to its low level. -Amplitude height from baseline. Floyd, Digital Fundamentals, 10th ed © 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved Summary Pulse Definitions Actual pulses are not ideal but are described by the rise time, fall time, amplitude, and other characteristics. Overshoot Ringing Droop 90% Amplitude tW 50% Pulse width 10% Ringing Base line Floyd, Digital Fundamentals, 10th ed Undershoot tr tf Rise time Fall time © 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved Summary Periodic Pulse Waveforms Periodic pulse waveforms are composed of pulses that repeats in a fixed interval called the period. The frequency is the rate at which it repeats it self and is measured in hertz. Floyd, Digital Fundamentals, 10th ed © 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved Summary Pulse Definitions In addition to frequency and period, repetitive pulse waveforms are described by the amplitude (A), pulse width (tW) and duty cycle. pulse width (tw) is a measure of the duration of the pulse Duty cycle is the ratio of pulse width (t)W to period (T). Volts Amplitude (A) Pulse width (tW) Time Period, T Floyd, Digital Fundamentals, 10th ed © 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved Summary Digital Waveform Carries Binary Information Bit time each bit in a sequence occupies a defined time interval. The clock is a basic timing signal that is an example of a periodic wave. Floyd, Digital Fundamentals, 10th ed © 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved Summary Timing Diagrams A timing diagram is graph of digital waveforms showing the actual time relationship of two or more waveforms and how each waveform changes on relation the others. Clock A B C A diagram like this can be observed directly on a logic analyzer. Floyd, Digital Fundamentals, 10th ed © 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved Summary Serial and Parallel Data Data refers to groups of bits, which represented by digital waveforms must be transferred from one circuit to another(from memory to CPU), can be transferred by either serial transfer (sent one bit at a time) or parallel transfer(all bits in a group are sent at the same time). 1 Computer Printer 0 1 t0 0 t1 1 t2 1 t3 0 t 4 t5 Computer 0 1 t6 1 0 t7 1 Modem 0 0 1 0 t0 Floyd, Digital Fundamentals, 10th ed t1 © 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved Summary Basic Logic Functions True only if all input conditions are true. True only if one or more input conditions are true. Indicates the opposite condition. Floyd, Digital Fundamentals, 10th ed © 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved Summary Basic System Functions And, or, and not elements can be combined to form various logic functions. A few examples are: The comparison function A Comparator A> B Two binary numbers A= B B A< B Basic arithmetic functions Adder A Two binary numbers B Carry in Floyd, Digital Fundamentals, 10th ed Outputs Σ Cout Sum Carry out Cin © 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved Summary Basic System Functions HIGH The encoding function Convert information such as decimal digit to binary code 7 4 8 1 2 3 0 . +/– 5 9 6 9 8 7 6 5 4 3 2 1 0 Encoder Binary code for 9 used for storage and/or computation Calculator keypad The decoding function Decoder Convert coded information such as Binary number to decimal form Binary input 7-segment display Floyd, Digital Fundamentals, 10th ed © 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved Summary Basic System Functions The data selection function Multiplexer A ∆t1 B Demultiplexer Data from A to D Data from B to E Data from C to F Data from A to D ∆ t1 ∆ t2 ∆ t3 ∆t 1 D ∆t1 E ∆t2 C ∆t2 ∆t3 ∆t3 Switching sequence control input Switching sequence control input F Multiplexer Switches digital data from several input lines onto a single output line Demultiplexer Switches digital data from one input line to several output lines Floyd, Digital Fundamentals, 10th ed © 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved Summary Basic System Functions The counting function Counter 1 2 3 4 Input pulses 5 Parallel output lines Binary code for 1 Binary code for 2 Binary code for 3 Binary code for 4 Binary code for 5 Sequence of binary codes that represent the number of input pulses counted. …and other functions such as code conversion and storage. Floyd, Digital Fundamentals, 10th ed © 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved Summary Integrated Circuits All the logic elements and functions that have been discussed are generally available in integrated circuit (IC) form. integrated circuit (IC) : Is an electronic circuit that is constructed entirely on a single small chip of silicon Chip Plastic case Pins Fixed-function logic and Programmable logic are two broad categories of digital ICs Floyd, Digital Fundamentals, 10th ed © 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved Summary Fixed-function logic Fixed-function logic A category of digital integrated circuits having functions that cannot be altered. The logic functions are set by the manufacturer and cannot be altered Floyd, Digital Fundamentals, 10th ed © 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved Summary Programmable Logic Programmable logic devices (PLDs) are an alternative to fixed function devices. The logic can be programmed for a specific purpose. In general, they cost less and use less board space that fixed function devices. Floyd, Digital Fundamentals, 10th ed © 2009 Pearson Education, Upper Saddle River, NJ 07458. All Rights Reserved