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CT1037NCT1037NIntroduction to CommunicationsIntroduction to Communications
Digital Signals & Binary Digital Signals & Binary CodesCodes
Er. Saroj Sharan RegmiEr. Saroj Sharan Regmi
Lecture 06Lecture 06
Last Lecture: 05Last Lecture: 05Signal Representation & Spectral AnalysisSignal Representation & Spectral Analysis
• Signals and Systems,
• Continuous- and Discrete- Time Systems,
• Continuous- and Discrete- Time Signals,
• Fourier Series,
• One-Sided Amplitude Frequency Spectrum,
• Two- Sided Amplitude Frequency Spectrum.
Today’s Lecture: 06Today’s Lecture: 06Digital Signals & Binary CodesDigital Signals & Binary Codes
• Review Signals & Analogue Signals.
• Digital Signals.
• Advantages of Digital Signals.
• Binary Digital Signals.
• Binary Signal Ratios.
• Data Codes.
• Data Coding Efficiency.
• Data Coding Noise Immunity.
• Bit Error Rate.
• Encoding Schemes.
SignalsSignals
• Signal: An electrical voltage or current which varies with time and is used to carry messages or information from one point to another.
• Analogue signals represent information by varying continuously with time.
Analogue SignalsAnalogue Signals
• Noise added to the analogue signal can greatly affect the accuracy of the information.
• Limiting the level of noise is not an easy or inexpensive process.
• Digital signals vary abruptly and change between distinct voltage or current levels.
Digital SignalsDigital Signals
• The most widely used form of a digital signal is binary, (two states).
Usually represented as 0 Volts (0V) and 5 Volts (+5V),
Also as: 0 & 1, Low & High, OFF & ON, False & True.
• Information is represented as a train of pulses arranged in specific combinations.
• A digital waveform can decrease the effect of noise on the information to a very great effect.
Advantages of Digital SignalsAdvantages of Digital Signals
• A digital waveform is less sensitive to noise than an analogue signal:
Decreases the effect of noise on the information to a very great effect.
• Less cross-talk (co-channel interference).
• Lower distortion levels.
• Faded signals are more easily recreated.
• Greater transmission efficiency.
Binary Digital SignalsBinary Digital Signals
• Signals arising from computer type equipment designed to transmit information in coded form.
• Bits: The individual 1's and 0's.
• Bit Slot Duration, : The time required by each bit to be transmitted.
τ
0 1 0 1 0 1 0 1
τ
Bandwidth in Digital SignalsBandwidth in Digital Signals
• Binary Digital Systems:
Bit Rate: The number of bits transmitted per second.
Bit Rate =1τ
… (bps )
• Other (Non-Binary) Digital Systems:
Baud Rate: The number of symbols transmitted per second.
Each symbol is composed of more than 1 bit.
: the 1 bit slot duration,
T : the periodic time,
T - :the 0 bit slot duration.
τ
τ
Binary Signal RatiosBinary Signal Ratios
• Ratios in Binary Signals enable us to see the relationship between a bit set at 1 and another set at 0.
0 1 0 1
τ
T
• The ratio between the 1's and the periodic time of one cycle.
Expressed as a percentage of period.
Mark Space Ratio = τ : T − τ = 1 :?
Duty C ycle = τ : T = ?%
• The ratio between the 1's and the 0's.
used in Morse Code.
Mark Space RatioMark Space Ratio
Duty-Cycle RatioDuty-Cycle Ratio
What is the mark-space ratio and the duty-cycle of a binary transmission with periodic time T = 1 ms when = 200 µs ?
T = 1 ms
= 200 µs = 0.2 ms Mark Space Ratio = τ : T − τ= 200×10−6 : (1×10−3−200×10−6 )=¿ 200×10−6 : 8×10−4 = 1 : 4Mark Space Ratio = 1 : 4
Duty Cycle = τ : T= 200×10−6 : 1×10−3 = 1 : 5Duty Cycle = 1 : 5 = 20
τ
τ
Binary Signal Ratios: ExampleBinary Signal Ratios: Example
Data CodesData Codes
• Data codes have always been in widespread use even since mankind’s early history:
From the use of hand signals to mirror flashing signals across the land, to smoke signals of the American Indians, information has been coded and sent by a variety of means.
• Data codes are the way in which bits are grouped together to represent different symbols.
• The sender and receiver must use the same code in order to communicate properly.
• ASCII is the most widespread data code in use today:
7-bit code that can represent a total of 128 symbols(27 = 128).
Limited by the number of symbols it can represent.
Number of bits in a Data CodeNumber of bits in a Data Code
• The number of bits in a code will dictate the maximum number of symbols which can be represented.
• Alternatively, the maximum number of symbols required will dictate the number of bits that must be included in a code.
2n = M … or … n= log2Mn = number of bits in a code
M = number of symbols represented
Number of bits in a Data Code (…2)Number of bits in a Data Code (…2)
CodeCode bits in Codebits in Code Maximum Number of SymbolsMaximum Number of Symbols
BCD 4 24 = 16
BAUDOT 5 25 = 32
? 6 26 = 64
ASCII 7 27 = 128
EBCDIC 8 28 = 256
? 10 210 = 1024
UNICODE 16 216 = 65536
Data Coding EfficiencyData Coding Efficiency
• The efficiency with which a code can be used to represent a group of symbols.
• Based on:
the number of symbols requiring representation, and
the number of bits that a code must have to enable the representation of all symbols.
coding efficiency (μ )=bits neededbits used
×100
• How many bits would be required to distinguish the 88 keys of a piano and what would the coding efficiency be?
n=log 2M=log10M
log102=log1088
log102=1 .9440 .301
=6 .46 bits … (7 bits )
coding efficiency (μ )=6 .46 bits7 bits
×100 =92.3
Data Coding Efficiency: Example 1Data Coding Efficiency: Example 1
Data Coding Efficiency: Example 2Data Coding Efficiency: Example 2
• Compare the efficiency of the binary versus the decimal coding systems when representing the 26 letters of the alphabet:
n=log 2M=log10M
log102=log1026
log102=1 .4140 .301
=4 .7 bits …(5 bits )
coding efficiency (μ )=4 .7 bits5 bits
×100 =94
n= log 10M = log 10 26= 1 . 415 d its … ( 2 d its )
coding efficiency (μ )=1 .415 dits2 dits
×100 =71
• The binary code:
• The decimal code:
Data Coding Noise ImmunityData Coding Noise Immunity
• Binary coding is more immune to noise than any other form of coding.
The Binary Code: The Decimal Code:
0V
10V
Threshold = 0.5V
Threshold = 5V
• Consider the example below:
Bit Error Rate (BER)Bit Error Rate (BER)
• BER relates to the number of possible erroneous bits received.
• Shows the quality of a particular communications link.
BER=Number of Erroneous Bits ReceivedTotal Number of Bits Transmitted
• BER values for a digital transmission system are normally specified and depend on the Signal-to-Noise Ratio (SNR) of the detection system.
• A typical BER requirements is in the region of 10-9.
• BER is an error probability defined as:
Bit Error Rate (BER): ExampleBit Error Rate (BER): Example
• Example: What is the BER of a transmission consisting of 5Gb if the erroneous bits received are 3?
BER =3
5×109= 0 . 0000000006 = 6×10−10
Morse CodeMorse Code
• One of the first character codes developed.
• A crude but effective way of transmitting characters over a telegraph circuit.
• Developed with a telegraph operator in mind who:
sent combinations of dots (short beep) and dashes (long beep),
paused for a short time between letters.
• Unsuitable for computer communications:
due to the extra time required between the transmission of each character,
limiting number of characters that could be represented.
Morse Code (…2)Morse Code (…2)
Baudot CodeBaudot Code
• One of the first character codes developed with machines in mind.
• Uses 1s and 0s to represent characters.
• Uses 5 bits of information per character.
• Case sensitive:
lower case characters represent letters,
upper case characters represent figures.
• Results in 32 different characters per case.
• Used for many years on telex equipment and is still used on some teletype machines.
• Unsuitable for high speed data communications due to the time required to switch between cases.
Baudot Baudot Code (…Code (…
2)2)
BCDBCD(Binary Coded Decimal)(Binary Coded Decimal)
• 4-bit code which allows for up to 16 characters / symbols (24 = 16).
• Often used to represent digits 0 to 9 but insufficient number of characters for anything else.
• 6-bit version allows for up to 64 characters.
EBCDICEBCDIC(Extended Binary Coded Decimal Interchange (Extended Binary Coded Decimal Interchange
Code)Code)• 8-bit standard which allows for up to 256 characters (28 =
256).
• Not all codes are used hence gaps exist.
• Common on IBM mainframes and related products.
ASCIIASCII(American Standard Code for Information Interchange)(American Standard Code for Information Interchange)
• The ASCII code is the most popular code for serial data communications today.
• It is a 7-bit code allowing up to 128 combinations (27 = 128), and thus supports upper and lowercase characters, numeric digits, punctuation symbols, and special codes.
• ASCII is also used as the data code for keyboards in computers.
• Control codes are used and are represented as symbols.
Used in binary synchronous communication, and device control codes in communicating with devices such as printers or terminals.
The 7-bit ASCII CodeThe 7-bit ASCII Code
©
C i s
c o
S
y s
t e
m s
,
I n
c .
Data (Line) EncodingData (Line) Encoding
• Data encoding puts the coded information into a form which will enable its transfer through a certain medium.
The simplest data encodings have undesirable timing and electrical (dc) characteristics.
• Line codes have been designed to have desirable transmission properties.
Bi-phase encoding transition, such as the Manchester encoding, has no dc component whatever the word transmitted thus offering desirable electrical characteristics.
• Both digital and analogue data can be encoded into various forms.
• Data encoding describes how the bits are actually signalled on the wire.
Different signal elements are used to represent binary 1 and binary 0.
• Encoding scheme is the mapping from binary digits to signal elements.
minimizes errors in determining the start and end of each bit,
minimizes errors in determining whether each bit is 1 or 0.
Data (Line) Encoding (…2)Data (Line) Encoding (…2)
• There are various techniques for data encoding:
TTL: Transistor-Transistor Logic,
NRZ-L: Non-Return to Zero-Level,
NRZI: Non-Return to Zero-Inverted,
Manchester Tx (+),
Manchester Tx (-),
Differential Manchester,
MLT3: Multi-Level Threshold-3,
etc.
Data Encoding SchemesData Encoding Schemes
Data Encoding Schemes (…2)Data Encoding Schemes (…2)
Data Encoding Schemes (…3)Data Encoding Schemes (…3)
Data Encoding Schemes (…4)Data Encoding Schemes (…4)
SummarySummary
• Defined Digital Signals.
• Characteristics of Binary Digital Signals.
• Reviewed the Mark Space Ratio and the Duty Cycle mechanisms.
• Data encoding efficiency.
• Data codes are the way in which bits are grouped together to represent different symbols. Examples are Morse, Baudot, BCD, EBCDIC, ASCII, etc.
• Binary coding is more immune to noise than any other form of coding.
• Data Encoding puts the coded information into a form which will enable its transfer through a certain medium.
• Examples of Encoding Schemes are TTL, NRZ-L, NRZI, Manchester Tx (+), Manchester Tx (-), Differential Manchester, MLT3, etc.