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Understanding Digital Systems

The following is an article based on a short presentation (PowerPoint) on Understanding Digital Systems. The article may serve as a guide on how to understand digital systems better, walking you through the building blocks of digital systems for you to understand them properly.

You can find the link to download the complete presentation at the end of this article.

1. What are Digital Systems

What are the systems that can be considered as Digital Systems? Personal Computers? Mobile Phones?

What are Digital Systems

Yes, Personal computers and mobile phones can be thought as digital systems. But what these digital systems have in common? What characterizes a digital system? Let’s discuss some concepts related to digital systems which may serve as the building blocks to extend our understanding about digital systems.

2. Measurements

We measure an attribute of some object. We get a value and the corresponding unit.

Measuring Weight

We use measurement tools to measure physical attributes of objects. An electronic scale can be used to measure the weight of a box. A ruler can be used to measure the length of a pen. By measuring, we get a value and a unit of the measurement. Let’s consider three different cases of measuring things and our expectations of the measurement.

Measurement (from Old French, mesurement) is the assignment of numbers to objects or events. It is a cornerstone of most natural sciences, technology, economics, and quantitative research in other social sciences. The science of measurement is called metrology.

Read more about Measurements

2.1. Measuring the Weight of a Box

Measuring Weight

The first case, measuring the weight of a box, is done with an electronic scale. We get the weight of the box, a value and a unit. It could be 2.1kg, 2.11kg, 2.136kg. Now, we have the value and the unit of the measurement. What had been our expectation about the value before the measurement was done? We expected it to be within a possible continuous range. We did not expect it to be a discrete value.

2.2. Frequencies after exciting a Hydrogen Atom

Exciting a Hydrogen Atom

The emission spectrum of atomic hydrogen is divided into a number of spectral series, with wavelengths given by the Rydberg formula. These observed spectral lines are due to electrons moving between energy levels in the atom.

Read more about Hydrogen Spectral Series

The second case, we are now exciting a hydrogen atom. We measure the output frequencies when the electrons return to their ground states. Now, we have the the values(frequencies) and the unit(hz). What had been our expectation about the values before the measurement was done? We expected to them to be discrete values. We did not expect the frequencies to be some arbitrary values.

2.3. Measuring IQ

The third case, measuring IQ of a group of students, is done using an IQ MCQ paper. We evaluate their choices in MCQs and assign marks based on whether their choice being right or wrong. Then we classify the students according to their total marks. At the end of the evaluation, we have one of the discrete levels assigned to each of the students for their IQ.

Measuring IQ

In the first case, our expectation was to have some arbitrary value as the measurement. But in the second case, we knew the quantum nature of the case and we expected the frequencies to be discrete values. As we can now see, our expectation varied depending on the nature of the system that we were measuring. Both the first and the second systems were natural. We measured something natural out of a system that was natural.

The third case was quite different from the first two cases for it was an artificial system that we implemented ourselves for evaluating IQ of the students. But our expectation of the final result was, finally, a discrete value. It can now be understood that, no matter whether the case is natural or artificial, our expectation of the measurement values can only be either continuous or discrete.

3. Classification of Systems

In teaching Signals and Systems, systems are often classified according to the output they produce in response to an input. i.e. We learn about discrete time systems having discrete time input signals and continuous time systems having continuous time input signals.

We use Laplace transform and Z transform to ease the analysis of continuous and discrete systems respectively. Let’s not dive that deeper into classifying the systems in this article. Let’s continue our classification based on the measurement that we made in the previous paragraphs.

When measuring, continuous values are expected from continuous systems and discrete values are expected in discrete systems. Yes, quite a simple classification, but it serves its purpose.

Systems Classification

Laplace Transform

Laplace Transform

The Laplace transform is a widely used integral transform in mathematics with many applications in physics and engineering. It is a linear operator of a function f(t) with a real argument t (t ≥ 0) that transforms f(t) to a function F(s) with complex argument s, given by the above integral.

Laplace Transform

Z Transform

Z Transform

The basic idea now known as the Z-transform was known to Laplace, and re-introduced in 1947 by W. Hurewicz as a tractable way to solve linear, constant-coefficient difference equations. It was later dubbed “the z-transform” by Ragazzini and Zadeh in the sampled-data control group at Columbia University in 1952.

Z Transform

4. Numeral Systems

We use decimal system for our day to day expression of numerical values. In the decimal system, we have 10 symbols to represent our values. [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]

Numeral Systems

Let’s take 200 symbol as an example. While it can be thought as a symbol itself in its entirely i.e. 200, it can also be thought as having composed of 2 different symbols that are 2 and 0. The value expressed in the symbol 200 depends on which numeral system it has been written. As a general rule, the expressed value of a symbol depends on the numeral system being used and the position of the symbol in the presentation.

A numeral system (or system of numeration) is a writing system for expressing numbers, that is, a mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner. It can be seen as the context that allows the symbols “11” to be interpreted as the binary symbol for three, the decimal symbol for eleven, or a symbol for other numbers in different bases.

Read more about Numeral Systems

5. Binary Digital Systems

In a binary digital system, we only have 2 digits to represent values; 0 and 1.

Binary Digital Systems

6. Layered Model for Digital Systems

Layered Model

7. Presentation Summary

Presentation Summary

8. Questions and Answers

Q: We were made aware of the possibility of realizing ternary digital systems. Are you aware of any physical layer device available to implement such a system; or is there any research currently being done on ternary digital devices?

A: Please go thorough the following resources to find out more about ternary digital systems.

1. Design of Parallel Analog to Digital Converters for Ternary CMOS Digital Systems

2. Formal Verification of Digital Circuits Using Symbolic Ternary System Models

Thank You!

You can download the complete PowerPoint(.pptx) presentation (Understanding Digital Systems) using the below button. The download will contain all the above slides and a few more which was not discussed in the article.

Download the Presentation

Session Initiation Protocol

Telecommunication Signalling over the Internet Protocol since 1999.


Session Initiation Protocol (SIP) has roots in the IP community rather than telecommunications community.

Many other VoIP signalling protocols have been defined by telecommunications community (International Telecommunications Union – ITU) such as H.323 and BICC.

But SIP was standardized by the IP community (Internet Engineering Task Force – IETF).


SIP Protocol Designers

Henning Schulzrinne

Henning Schulzrinne

Henning Schulzrinne is the Chief Technology Officer (CTO) for the United States Federal Communications Commission. Previously he was chair of the Computer Science department at Columbia University. He is a co-chair of the Internet Technical Committee of the IEEE Communications Society.

Henning Schulzrinne Website

Mark Handley

Mark Handley

Mark Handley is Professor of Networked Systems in the Department of Computer Science of University College London since 2003, where he leads the Networks Research Group. He holds a Royal Society Wolfson Research Merit Award as well as a Roger Needham Award.

Mark Handley Website

The Protocol Design

In a SIP world, all are User Agents. SIP is a Peer-To-Peer protocol!

SIP is Peer-To-Peer: SIP requires only a Simple Core Network with intelligence distributed to the network edge, embedded in endpoints . SIP features are implemented in the communicating endpoints.

User Agent Client (UAC)

UAC generates requests and send them to servers.

Multifunctional UA: A single User Agent may function both as a client and as a server.

SIP Requests

  • REGISTER: Used by a UA to indicate its current IP address and the URLs for which it would like to receive calls.
  • INVITE: Used to establish a media session between user agents.
  • ACK: Confirms reliable message exchanges.
  • CANCEL: Terminates a pending request.
  • BYE: Terminates a session between two users in a conference.
  • OPTIONS: Requests information about the capabilities of a caller, without setting up a call.
  • PRACK (Provisional Response Acknowledgement): PRACK improves network reliability by adding an acknowledgement system to the provisional Responses (1xx). PRACK is sent in response to provisional response (1xx).

SIP Responses

  • Provisional (1xx): Request received and being processed.
  • Success (2xx): The action was successfully received, understood, and accepted.
  • Redirection (3xx): Further action needs to be taken (typically by sender) to complete the request.
  • Client Error (4xx): The request contains bad syntax or cannot be fulfilled at the server.
  • Server Error (5xx): The server failed to fulfill an apparently valid request.
  • Global Failure (6xx): The request cannot be fulfilled at any server.

User Agent Server (UAS)

UAS gets requests, processes those requests and generate responses.

There are four basic types of SIP servers.

  • 1. Proxy Server: Proxy servers are the most common type of servers in a SIP world. When a request is generated, the exact address of the recipient is not known in advance. So the client sends the request to a proxy server. The server on behalf of the client (as if giving a proxy for it) forwards the request to another proxy server or the recipient itself.
  • 2. Redirect Server: A redirect server redirects the request back to the client indicating that the client needs to try a different route to get to the recipient. It generally happens when a recipient has moved from its original position either temporarily or permanently.
  • 3. Registrar: One of the main jobs of the servers is to detect the location of a user in a network. How do they know the location. If you are thinking that users have to register their locations to a Registrar server, you are absolutely right. Users time to time refreshes their locations by registering (sending a special type of message) to a Registrar server.
  • 4. Location Server: The addresses registered to a Registrar are stored in a Location Server.

SIP is a Text-Based Protocol with syntax similar to that of HTTP or SMTP. There are two different types of SIP messages: requests and responses.

SIP is an Application Layer Protocol designed to be independent of the underlying transport layer. SIP can run on Transmission Control Protocol (TCP), User Datagram Protocol (UDP) or Stream Control Transmission Protocol (SCTP).

SIP works in conjunction with several other application layer protocols that identify and carry the Session Media. Media identification and negotiation is achieved with the Session Description Protocol (SDP). For the transmission of media streams (voice, video) SIP typically employs the Real-time Transport Protocol (RTP), which may be secured with the Secure Real-time Transport Protocol (SRTP). For secure transmissions of SIP messages the protocol may be encrypted with Transport Layer Security (TLS).

SIP Phones

Telecommunication with Sofware Phones

Ekiga SIP Phone
Call Me sip:udssl@ekiga.net
Ekiga Logo

The figure shows an Ekiga SIP Phone on Unix.


Free Your Speech!

Capturing REGISTER method with WireShark


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