Table of Contents

1 Table of ContentsLesson No. 011An Overview & Number Systems1 Programmable Logic Devices (PLDs)8 Fractions in Binary Number System13 Binary Number System12 Caveman number system11 Decimal Number System10 Number Systems and Codes10 Analogue to Digital and Digital to Analogue conversion and Interfacing9 Sequential logic and implementation8 Combinational Logic Circuits and Functional Devices7 Binary Number System4 Digital Systems and Digital Values4 Electronic Processing of Continuous and Digital Quantities3 Digital representing of quantities1 Analogue versus Digital1 Lesson No. 0214 Number Systems14 Binary to Decimal conversion14 Decimal to Binary conversion15 Converting Decimal fractions to Binary16 Binary Arithmetic17 Signed and Unsigned Binary Numbers191 s & 2 s complement20 Lesson No. 0323 Floating-Point Numbers24 Hexadecimal Numbers27 Lesson No. 0431 Octal Numbers31 The Excess Code34 The BCD Code34 The Gray Code36 Alphanumeric Codes37 ASCII Code38 Extended ASCII Code38 Parity Method38 Lesson No.

2 0540 Logic Gates40 AND Gate40OR Gate42 NOT Gate43 NAND Gate45 NOR Gate47 Lesson No. 0650 Logic Gates & Operational Characteristics50 Exclusive-OR and Exclusive-NOR Gates53 Digital Circuits and Operational Characteristics56 TTL/CMOS NOT Gate Operation57 Integrated Circuit Technologies57 Lesson No. 0761 Digital Circuits & Operational Characteristics61 Lesson No. 0871 Boolean Algebra & Logic Simplification71 Laws of Boolean Algebra72 Rules of Boolean Algebra73 Demorgan s Theorems74 Simplification using Boolean Algebra76 Standard Form of Boolean Expressions77 Lesson No. 0979 Standard SOP form84 Standard POS form85 Converting to Standard SOP and POS forms85 Minterms and Maxterms85 Lesson No. 1089 Karnaugh Map & Boolean Expression Simplification89 The 3-variable Karnaugh Map89 The 4-variable Karnaugh Map89 Grouping and Adjacent Cells90 Simplification of SOP expressions using the Karnaugh Map93 Don t care Conditions96 Lesson No.

3 1199 Five-Variable Karnaugh Map1027-Segment Display103 Lesson No. 12109 Comparators109 Quine-McCluskey Simplification Method110 Comparator Circuit116 Lesson No. 13118 Odd-Prime Number Detector118 Lesson No. 14131 Operation of Odd-Parity Generator Circuit132 XOR and XNOR Gates133 Half Adder and Full Adder134 Parallel Binary Adders137 Carry Propagation137 Lesson No. 15141 BCD ADDER141 Arithmetic and Logic Unit (ALU)147 Lesson No. 1615016-BIT ALU150 Comparators152 Decoders157 Binary Decoder158 MSI Decoder159 Lesson No. 17160 THE 74XX138 3-TO-8 DECODER160 BCD to 7-Segment Decoder162 MSI Seven-Segment Decoder163 BCD-to-Decimal Decoder163 Encoder163 Binary Encoder163 Priority Encoders164 Decimal-to-BCD Encoder166 Multiplexer167 Lesson No. 18169 Applications of Multiplexers172 Lesson No. 19178 Demultiplexer178 Applications of Demultiplexer178 Programmable Logic Devices179 Programmable Arrays of AND Gates and OR Gates179 Programmable Read-Only Memory (PROM)182 Programmable Logic Array (PLA)182 Programmable Array Logic (PAL)182 Generic Array Logic (GAL)183 Lesson No.

4 20190 The GAL22V10194 OLMC Combinational Mode196 Tri-State Buffers196 Lesson No. 21200 ABEL203 Boolean Operations and Boolean Notations203 Test Vectors206 Lesson No. 22209 Latches and Flip-Flops211 The NAND gate based S-R (Set-Reset) Latch211 The NOR gate based S-R (Set-Reset) Latch213 Lesson No. 23217 The Gated S-R Latch218 The Gated D Latch219 Edge-Triggered Flip-Flop221 Edge-Triggered S-R Flip-flop222 Edge-Triggered D Flip-flop224 Edge-Triggered J-K Flip-flop225 Master-Slave Flip-Flops230 Lesson No. 24237 Edge-Triggered J-K Flip-flop240J-K flip-flop used as a counter246 Lesson No. 25248 One-Shot Mono-stable multi-vibrator255 Lesson No. 26258 THE 555 TIMER258 Counters261 asynchronous Counters (Ripple Counters)262 Mod-n Counters265 Integrated Circuit asynchronous Counters268 Lesson No. 27270 Down Counters270 synchronous Counters272 Lesson No. 28277 Mod-n synchronous Counter277 Integrated Circuit synchronous Counters278 Cascading Counters279 Lesson No.

5 29286Up/Down Counters286 design Procedure298 Lesson No. 30305 Digital Clock305 Lesson No. 31314S-R flip-flop based Implementation316 Lesson No. 32320 State Reduction325 Lesson No. 33328 State Assignment328 Moore Machine State Diagram330 Mealy Machine333 Lesson No. 34339 Shift Registers339 Serial In/Shift Right/Serial Out Operation339 Serial In/Shift Left/Serial Out Operation339 Serial In/Parallel Out Operation341 Parallel In/Serial Out Operation343 Parallel In/Parallel Out Operation345 Rotate Right Operation347 Rotate Left Operation347 Shift Register Counters347 Johnson Counter347 Ring Counter348 Lesson No. 35349 Serial-to-Parallel Converter349 Keyboard Encoder350 Lesson No. 363603-Bit Up/Down Counter360 Elevator State Diagram366 Lesson No. 37370 Traffic Signal Control System374 Lesson No. 38378 Equation Definition378 Lesson No. 39387 Memory387 Memory Organization387 Random Access Memory (RAM)391 Static RAM392 Lesson No.

6 40396 Dynamic RAM400 Lesson No. 41405 Types of DRAMs407 ROM Read-Only Memory407 PROM (Programmable ROMs)410 EPROM Erasable PROM411 Programming EPROM412 EEPROM Electrically Erasable PROM412 FLASH Memory412 Lesson No. 42416 Flash Memory Array416 First In-First Out (FIFO) Memory418 Lesson No. 43422 Last IN - First OUT (LIFO) Memory422 Memory Map424 Address Decoders428 Introduction to FPGAs430 Lesson No. 44432 Analogue to Digital Conversion434 Operational Amplifier (Op-Amp)439 Lesson No. 45446 Digital to Analogue Conversion449CS302 - Digital Logic & design Lesson No. 01 AN OVERVIEW & NUMBER SYSTEMS Analogue versus Digital Most of the quantities in nature that can be measured are continuous. Examples include Intensity of light during the da y: The intensity of light gradually increases as the sun rises in the morning; it remains constant throughout the day and then gradually decreases as the sun sets until it becomes completely dark.

7 The change in the light throughout the day is gradual and continuous. Even with a sudden change in weather when the sun is obscured by a cloud the fall in the light intensity although very sharp however is still continuous and is not abrupt. Rise and fall in temper ature during a 24-hour period: The temperature also rises and falls with the passage of time during the day and in the night. The change in temperature is never abrupt but gradual and continuous. Velocity of a car travelling from A to B: The velocity of a car travelling from one city to another varies in a continuous manner. Even if it abruptly accelerates or stops suddenly, the change in velocity seemingly very sudden and abrupt is never abrupt in reality. This can be confirmed by measuring the velocity in short time intervals of few milliseconds. The measurable values generally change over a continuous range having a minimum and maximum value.

8 The temperature values in a summer month change between 23 0C to 45 0C. A car can travel at any velocity between 0 to 120 mph. Digital representing of quantities Digital quantities unlike Analogue quantities are not continuous but represent quantities measured at discrete intervals. Consider the continuous signal as shown in the figure To represent this signal digitally the signal is sampled at fixed and equal intervals. The continuous signal is sampled at 15 fixed and equal intervals. Figure The set of values (1, 2, 4, 7, 18, 34, 25, 23, 35, 37, 29, 42, 41, 25 and 22) measured at the sampling points represent the continuous signal. The 15 samples do not exactly represent the original signal but only approximate the original continuous signal. This can be confirmed by plotting the 15 sample points. Figure The reconstructed signal from the 15 samples has sharp corners and edges in contrast to the original signal that has smooth curves.

9 If the number of samples that are collected is reduced by half, the reconstructed signal will be very different from the original. The reconstructed signal using 7 samples have missing peak and dip at 34 0C and 23 0C respectively. Figure The reason for the difference between the original and the reconstructed signal is due to under-sampling. A more accurate representation of the continuous signal is possible if the number of samples and sampling intervals are increased. If the sampling is increased to infinity the number of values would still be discrete but they would be very close and closely match the actual signal. Copyright Virtual University of Pakistan 1CS302 - Digital Logic & design Figure Continuous signal showing temperature varying with time Figure Sampling the Continuous Signal at 15 equal intervals 0510152025303540451 2 3 4 5 6 7 8 9 101112131415timetemperature 0C12473425233729424125221835051015202530 354045123456789101112131415timetemperatu re 0C Copyright Virtual University of Pakistan 2CS302 - Digital Logic & design Figure Reconstructed Signal by plotting 15 sampled values Figure Reconstructed Signal by plotting 7 sampled values Electronic Processing of Continuous and Digital Quantities Electronic Processing of the continuous quantities or their Digital representation requires that the continuous signals or the discrete values be converted and

10 Represented in terms of voltages. There are basically two types of Electronic Processing Systems. Analogue Electronic Systems: These systems accept and process continuous signals represented in the form continuous voltage or current signals. The continuous quantities are converted into continuous voltage or current signals by transducers. The block diagram describes the processing by an Analogue Electronic System. Figure 1247183425233537294241252205101520253035 4045123456789101112131415samplestemperat ure 0C05101520253035404513579111315sampleste mperature 0C Copyright Virtual University of Pakistan 3CS302 - Digital Logic & design Digital Electronic Sy stems: These systems accept and process discrete samples representing the actual continuous signal. Analogue to Digital Converters are used to sample the continuous voltage signals representing the original signal.