Digital Logic & Design Dr. Waseem Ikram Lecture 01
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Digital Logic & Design
Dr. Waseem Ikram
Lecture 01
Analogue QuantitiesAnalogue Quantities
Continuous QuantityContinuous Quantity Intensity of LightIntensity of Light TemperatureTemperature VelocityVelocity
Digital ValuesDigital Values
Discrete set of valuesDiscrete set of values
Continuous SignalContinuous Signal
0
5
10
15
20
25
30
35
40
45
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
time
tem
per
atu
re
0 C
Continuous SignalContinuous Signal
1 24
7
34
2523
37
29
42 41
2522
18
35
0
5
10
15
20
25
30
35
40
45
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
time
tem
per
atu
re
0 C
Digital RepresentationDigital Representation
1 24
7
18
34
2523
3537
29
42 41
2522
0
5
10
15
20
25
30
35
40
45
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
samples
tem
per
atu
re
0 C
Under SamplingUnder Sampling
0
5
10
15
20
25
30
35
40
45
1 3 5 7 9 11 13 15
samples
tem
per
atu
re
0 C
Electronic ProcessingElectronic Processing
Analogue SystemsAnalogue Systems Digital SystemsDigital Systems Representing quantities in Digital SystemsRepresenting quantities in Digital Systems
Representing Digital ValuesRepresenting Digital Values
39 39 00C ?C ?
a1
1
a2
2 3a
3
4a
4
b1
b2
b3
b4
5 6 7 8
Vcc
10
GN
D 01mV = 1
39mV39mV
6.25 x 106.25 x 101515 V !! V !!
DigitalDigital SystemSystem
6.25 x 106.25 x 101818 ? ?
Digital SystemsDigital Systems
Two Voltage LevelsTwo Voltage Levels Two StatesTwo States
– On/Off– Black/White– Hot/Cold– Stationary/Moving
Binary Number SystemBinary Number System
Binary NumbersBinary Numbers Representing Multiple ValuesRepresenting Multiple Values Combination of 0v & 5vCombination of 0v & 5v
Merits of Digital SystemsMerits of Digital Systems
Efficient Processing & Data StorageEfficient Processing & Data Storage Efficient & Reliable TransmissionEfficient & Reliable Transmission Detection and Correction of ErrorsDetection and Correction of Errors Precise & Accurate ReproductionPrecise & Accurate Reproduction Easy Design and ImplementationEasy Design and Implementation Occupy minimum spaceOccupy minimum space
Information ProcessingInformation Processing
NumbersNumbers TextText Formula and EquationsFormula and Equations Drawings and PicturesDrawings and Pictures Sound and MusicSound and Music
Logic GatesLogic Gates
Building BlocksBuilding Blocks AND, OR and NOT GatesAND, OR and NOT Gates NAND, NOR, XOR and XNOR GatesNAND, NOR, XOR and XNOR Gates Integrated Circuits (ICs)Integrated Circuits (ICs)
Logic Gate Symbol and ICsLogic Gate Symbol and ICs
AND Gate OR Gate NOT Gate
1 2 3 4 5 6
GN
D
Vcc 13 12 11 10 9 8
7400
NAND Gate NOR Gate XOR Gate XNOR Gate
NAND Gate IC
Combinational CircuitsCombinational Circuits
Combination of Logic GatesCombination of Logic Gates Adder Combinational CircuitAdder Combinational Circuit
Adder Combinational CircuitAdder Combinational Circuit
Sum
Carry
Functional DevicesFunctional Devices
Functional DevicesFunctional Devices– Adders– Comparators– Encoders/Decoders– Multiplexers/Demultiplexers
Sequential CircuitsSequential Circuits
Memory ElementMemory Element Current & Previous StateCurrent & Previous State Flip-FlopsFlip-Flops Counters & RegistersCounters & Registers
Block Diagram of a Sequential Block Diagram of a Sequential CircuitCircuit
a11
a22
b1
b2
5
6CombinationalLogic Circuit
OutputInput
a11
b15
Memory Element
Programmable Logic Devices (PLDs)Programmable Logic Devices (PLDs)
Configurable HardwareConfigurable Hardware Combinational CircuitsCombinational Circuits Sequential CircuitsSequential Circuits Low chip countLow chip count Lower CostLower Cost Short development timeShort development time
MemoryMemory
Storage Storage RAM (Random Access Memory)RAM (Random Access Memory)
– Read-Write– Volatile
ROM (Read-Only Memory)ROM (Read-Only Memory)– Read-Only– Non-Volatile
A/D & D/A ConvertersA/D & D/A Converters
Processing of Continuous values Processing of Continuous values Conversion Conversion
– Analogue to Digital A/D– Digital to Analogue D/A
Industrial Control ApplicationIndustrial Control Application
Digital Industrial ControlDigital Industrial Control
DigitalDigital
ControllerController
ThermocoupleThermocouple
A/DA/DConverterConverter
u1x1
* / *
D/AD/AConverterConverter
u1x1
* / *
ReactionReactionVesselVessel
HeaterHeater
ControlControl
SummarySummary
Continuous SignalsContinuous Signals Digital Representation in BinaryDigital Representation in Binary Information ProcessingInformation Processing Logic GatesLogic Gates
Combinational & Sequential CircuitsCombinational & Sequential Circuits Programmable Logic Devices (PLDs)Programmable Logic Devices (PLDs) Memory (RAM & ROM)Memory (RAM & ROM) A/D & D/A ConvertersA/D & D/A Converters
SummarySummary
Number Systems and CodesNumber Systems and Codes
Decimal Number SystemDecimal Number System Caveman Number SystemCaveman Number System Binary Number SystemBinary Number System Hexadecimal Number SystemHexadecimal Number System Octal Number SystemOctal Number System
Decimal Number SystemDecimal Number System
Ten unique numbers 0,1..9Ten unique numbers 0,1..9 Combination of digitsCombination of digits Positional Number SystemPositional Number System 275 = 2 x 10275 = 2 x 1022 + 7 x 10 + 7 x 1011 + 5 x 10 + 5 x 1000
– Base or Radix 10– Weight 1, 10, 100, 1000 ….
Representing FractionsRepresenting Fractions
Fractions can be represented in decimal Fractions can be represented in decimal number system in a mannernumber system in a manner
= 3 x 10= 3 x 1022 + 8 x 10 + 8 x 1011 + 2 x 10 + 2 x 1000 + 9 x 10 + 9 x 10-1-1
+ 1 x 10+ 1 x 10-2-2
= 300 + 80 + 2 + 0.9 + 0.01 = 300 + 80 + 2 + 0.9 + 0.01
= 382.91= 382.91
Caveman Number SystemCaveman Number System
∑∑, ∆, >, Ω and ↑, ∆, >, Ω and ↑ Base – 5 Number SystemBase – 5 Number System ∆∆Ω↑∑ = 220Ω↑∑ = 220
Caveman Number SystemCaveman Number System
Decimal Decimal NumberNumber
Caveman Caveman NumberNumber
Decimal Decimal NumberNumber
Caveman Caveman NumberNumber
00 ∑∑ 1010 >∑>∑
11 ∆∆ 1111 >∆>∆
22 >> 1212 >>>>
33 ΩΩ 1313 >Ω>Ω
44 ↑↑ 1414 >↑>↑
55 ∆∑∆∑ 1515 Ω∑Ω∑
66 ∆∆∆∆ 1616 Ω∆Ω∆
77 ∆∆>> 1717 Ω>Ω>
88 ∆∆ΩΩ 1818 ΩΩΩΩ
99 ∆↑∆↑ 1919 Ω↑Ω↑
Caveman Number SystemCaveman Number System
Mr. Caveman is using a base 5 number Mr. Caveman is using a base 5 number system. Thus the number ∆Ω↑∑ in system. Thus the number ∆Ω↑∑ in decimal isdecimal is
= ∆ x 5= ∆ x 533 + Ω x 5 + Ω x 522 + ↑ x 5 + ↑ x 511 + ∑ x 5 + ∑ x 500
= ∆ x 125 + Ω x 25 + ↑ x 5 + ∑ x 1 = ∆ x 125 + Ω x 25 + ↑ x 5 + ∑ x 1
= (1) x 125 + (3) x 25 + (4) x 5 + (0) x 1 = (1) x 125 + (3) x 25 + (4) x 5 + (0) x 1
= 125 + 75 + 20 + 0 = 220= 125 + 75 + 20 + 0 = 220
Binary Number SystemBinary Number System
Two unique numbers 0 and 1Two unique numbers 0 and 1 Base – 2Base – 2 A binary digit is a bitA binary digit is a bit Combination of bits to represent larger Combination of bits to represent larger
valuesvalues
Binary Number SystemBinary Number System
Decimal Decimal NumberNumber
Binary NumberBinary Number Decimal Decimal NumberNumber
Binary NumberBinary Number
00 00 1010 10101010
11 11 1111 10111011
22 1010 1212 11001100
33 1111 1313 11011101
44 100100 1414 11101110
55 101101 1515 11111111
66 110110 1616 1000010000
77 111111 1717 1000110001
88 10001000 1818 1001010010
99 10011001 1919 1001110011
Combination of Binary BitsCombination of Binary Bits
Combination of BitsCombination of Bits 100111001122 = 19 = 191010
= (1 x 2= (1 x 244) + (0 x 2) + (0 x 233) + (0 x 2) + (0 x 222) + (1 x 2) + (1 x 211) ) + (1 x 2+ (1 x 200))
= (1 x 16) + (0 x 8) + (0 x 4) + (1 x 2) = (1 x 16) + (0 x 8) + (0 x 4) + (1 x 2) + (1 x 1)+ (1 x 1)
= 16 + 0 + 0 + 2 + 1= 16 + 0 + 0 + 2 + 1= 19= 19
Fractions in BinaryFractions in Binary
Fractions in BinaryFractions in Binary 1011.1011011.10122 = 11.625 = 11.625
= (1 x 23) + (0 x 22) + (1 x 21) + (1 x 20) + (1 x 2-1) + (0 x 2-2) + (1 x 2-3)
= (1 x 8) + (0 x 4) + (1 x 2) + (1 x 1) + (1 x 1/2) + (0 x 1/4) + (1 x 1/8)
= 8 + 0 + 2 + 1 + 0.5 + 0 + 0.125= 11.625
Floating Point NotationsFloating Point Notations
Decimal-Binary ConversionDecimal-Binary Conversion
Binary to Decimal ConversionBinary to Decimal Conversion– Sum-of-Weights– Adding weights of non-zero terms
Decimal to Binary ConversionDecimal to Binary Conversion– Sum-of-Weights (in reverse)– Repeated Division by 2
NumberNumber WeightWeight Result after subtractionResult after subtraction Binary Binary
392392 256256 392-256=136392-256=136 11
136136 128128 136-128=8136-128=8 11
88 5454 00
88 3232 00
88 1616 00
88 88 8-8=08-8=0 11
00 44 00
00 22 00
00 11 00
Decimal to binary conversion using
Sum of weight
Decimal-Binary ConversionDecimal-Binary Conversion
2
4 3 2 1
0
10011
(1 2 ) (0 2 ) (0 2 ) (1 2 )
(1 2 )
Terms 16,0,0.2 and 1
19
Binary to Decimal ConversionBinary to Decimal Conversion– Sum-of-Weights– Adding weights of non-zero terms
Decimal-Binary ConversionDecimal-Binary Conversion
Binary to Decimal ConversionBinary to Decimal Conversion– Sum-of-Weights– Adding weights of non-zero terms
Binary to Decimal ConversionBinary to Decimal Conversion– Sum-of-Weights– Adding weights of non-zero terms
Decimal-Binary ConversionDecimal-Binary Conversion
2
2
10011 16 2 1 19
1 11011.101 8 2 2 8511 8
11.625
Lecture No. 1Lecture No. 1
Number SystemsNumber Systems
A SummaryA Summary