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Block 1 - Stress Calculations Formulae:

Design Load (N) = Normal Maximum Load (N) x Safety Factor

Stress (N / m 2) = Force (N) / Cross - sectional Area (m 2)

Strain = Change in length / Original Length, or (L2 - L1) / L1 x 100 expressed as a %

Stiffness (N mm -1) = Load (N) / Deflection (mm)

Young's Modulus (N mm -2) = Stress (N mm -2) / Strain, or Force (N) / Area (mm 2) x L1 / L2 - L1 up to the yield stress.

Moment (N m -1) = Force (N) x Distance from pivot (m)

For the purposes of stress calculations N mm -2 and MN m -2 are numerically equal.

Heat Load Calculations Formulae:

E (J) = mc (Temperature change) = Pt = Specific loss x Degree - Days x 86400
where E = energy flow, loss or requirement, as heat required must balance heat loss.

Heat capacity (J K-1) = Heat Flow (J)/ Temperature difference (K or oC)
(or mc)

Power (W) = Heat produced or used (J) / time (s)

Thermal conductivity (W m -1 oC-1) = Heat Flow Rate (W) x Thickness (m) / Area (m 2) x Temperature difference (K or oC)

Heat Flow Rate (W) = Area (m 2) x Temperature difference (oC) x Thermal conductivity (W m -1 oC -1) / Thickness (m)
Heat flow rate can be Ventilation loss or Fabric loss for a given calculation.

Ventilation Loss (W) = 0.33 x House volume (m 3) x a.c.h. x Temperature difference (oC).
(a.c.h. = air changes per hour, usually c. 1.5 to 2.5 for an averaged sized single- or 2-storey house)

Fabric Loss (W) = U - Value (W m2 oC) x Total net area (m 2) x Temperature difference (oC).

Total rate of heat loss (W) = Fabric loss (W) + Ventilation loss (W).

Specific loss (W oC) = Total rate of heat loss (W) / Temperature difference (oC)
i.e. specific loss of heat per degree temp. difference (oC).

Heat required (J) = Specific loss (W oC -1) x Degree - days x 86400, from above.

Specific Heat Capacity (J kg -1 K) = Gain in thermal energy (J) / Mass (kg) x Temperature Difference (K or oC).

U - Value (W m -2 oC -1) = Heat flow (J) / s through 1 m 2 of a building element per degree temperature difference across its thickness.

Block 2 - Introduction to Binary Conversion:

Limiting this example to a 10 - bit (or fewer) number, the following table may be set up:

2 9 2 8 2 7 2 6 2 5 2 4 2 3 2 2 2 1 2 0
512 256 128 64 32 16 8 4 2 1
0 0 1 1 0 0 1 0 1 1
0 0 128 64 0 0 8 0 2 1
Total = 203                

Binary numbers run from right to left, with the smallest unit 20 on the right. I have encoded for example the number 203, which is simply a matter of successively subtracting the highest power of 2 that is in the number:

203 - 128 =>(27) => value = 1
= 75 - 64 => (26) => 1
(25 value = 0 and 24 value = 0, to hold places)
= 11 - 8 => (23) => 1
(22 value = 0)
= 3 - 2 => (21) => 1
= 1 => (20) => 1

Each number in the second row is multiplied by the binary multiplier entered beneath it in the third row. The results are then entered in the fourth row, with zeros in the relevant places. The fourth row numbers are then summed to give the total in the fifth row. This method can be used to convert both ways.

The simplest binary state is either 1 = On, 0 = Off. In more sophisticated applications, a range of possible states may be required for performing functions. The number of states possible = 2n, where n is the number of bits per unit quantity. For pictures, the unit quantity may be pels, and the number of bits needed for each pel = n. So for a 16-colour picture at 4 bits per pel gives the 24 = 16 possible states for each pel. For a black and white image with no grey scale, each pel = 1 bit. For a 4-level grey scale each pel needs 2 bits: 22 = 4 levels.

Simplified conceptual view of a typical dial - up login connection to the Internet via an ISP:

Internet traffic routing
Login user connection
The modem feed has been split up between the different protocols for the diagram.

ADSL: Asynchonous data subcriber line - high data rate c. 2 Mbits s -1 downstream e.g. for distributing videos and information on demand.

Broadband - ISDN: A wide bandwidth version of ISDN which would enable packet - switched networks to integrate data and realtime speech by overcoming noticeable delays in data routing.

Fibre - optic cabling: A cable made up of specially designed filaments for carrying light pulses at speeds c. 2 x 10 8 m s -1. The signal pulses suffer little attenuation and can last longer distances before the need to be regenerated. FOC also allows higher signalling rates of light pulses, than switching voltages through copper wires.

ISDN: Integrated digital services network - circuit switched, uses existing copper telephone line and ISDN interface, 64 + 64 + 16 = 144 K bits s -1 duplex to the exchange. Analog speech can be digitalised in the telephone then sent.

Networks: WANs, LANs etc - Packet switched allowing multiple routing of data 'packets' to and from different users over a single section of circuit. An example of a WAN is the electronic banking system.

PSE: Packet switched exchange.

PSTN: Public switched telephone network (circuit switched)

PABX: Private automatic branch exchange - routes calls to and from internal extensions on the premises. Often a user on a PABX dials an assigned number for access to the PSTN.

1. The Internet and the World Wide Web (WWW):
The Internet is a system of electronic data transmission designed for use between computers or networks of computers over public telephone networks and allowing for multiple routing of data. It has expanded to become a global network of interconnected computer networks that communicate via Transmission Control Protocol and Internet Protocol (TCP / IP). Computers or networks themselves are referenced by unique host addressing as a domain number and / or subset of a domain. The Internet was developed originally by DARPA (Defense Research Projects Agency) and the US military to withstand nuclear attack. If a node or hub network was 'knocked out' multiple or alternative routing of data could be implemented.

The World Wide Web is a file and host referencing system based on Hyper Text Markup Language (HTML) which enables the use of embedded hypertext links to access files, documents, images, and addresses or other resources on the Internet. Hypertext Markup Language was developed initially by Tim Burners - Lee at CERN Particle Physics Laboratory. The main advantage of the WWW as opposed to earlier Internet - based file referencing systems such as Gopher, WAIS and other domain - specific systems, is its ability to access files or documents across domains with ease. Another big development was the development of the graphical browser user interface by Marc Andressen at NCSA. NCSA Mosaic (commercially marketed as Spyglass Mosaic) was the first proprietary browser later further developed as Netscape Mosaic (Netscape) and Windows Mosaic (Internet Explorer). Previously one had to manually enter file and host address strings using the standard Unix syntax. You sometimes may need to do that in specific cases e.g. "http://www.domainhostname/fileorpagename/", where 'http' specifies hypertext transfer protocol . Regardless of how accessed, this 'human readable' form of an address is resolved into that domain's unique IP address number e.g. 123.456.7.89

The main difference between the Internet and the WWW is that the Internet is primarily a data transmission system using TCP / IP that supports several protocols such as NNTP, FTP, SMTP, and HTTP, whereas the WWW is a file or Internet resource referencing system that is HTTP - specific. It is possible to reference a non - HTTP resource, in which case the relevant protocol will be activated usually as a separate program other than the browser coming up to handle the data transfer when the hypertext link is clicked on. An example of such would be "ftp://ftp.servername.filename" where File Transfer Protocol is specified. Similarly, one can connect to the Internet, without connecting to the WWW such as with a client connecting to a server through TCP / IP, e.g. a remote teleworker logging into the company's server to retrieve email.

An internal company network that uses Web - based technologies, but is protected from the outside by firewall proxies and gateways. The intranet is cross - platform integrated with internal legacy systems and applications such as company databases. It enables information to be updated easily, intuitive navigation and instant access by employees.

An extended intranet to include external company associates such as suppliers, clients or distributors, etc. This enables everyone to instantly access latest company information e.g. suppliers can access latest purchasing department's information.

2. Secret key and Public key Encryption:
Secret key encryption uses the same key to encrypt and decrypt a message. The strength of the encryption is only as good as the secrecy of the key. By using the cypher key to reverse the process of encryption one can decrypt the message. The weakness of secret key encryption lies in the need for secrecy in communication of the key to a recipient.

Public key encryption by contrast uses separate keys for encryption and decryption. The key for encryption can be communicated quite openly (public) without compromising security of encrypted messages as only the private key can decrypt messages. For example I received a message from my bank using my public key to encrypt:

Gm9Ot laM3QDA8hmK3L+z3buMhpFfr5thvoTbORhK/vAsoY=
(Sample PGP 1024 - bit encrypted text using standard cryptography and security lvl)

I 'unlock' the message with my unique private key and retrieve the plaintext message:

98765 Dear Sir, your account is overdrawn Please contact bank ASAP

Only my private key needs to be kept secret, and can possibly be itself encrypted under another key.

The main difference between private key cryptography and public key cryptography is that public key cryptography enables easier communication of encryption keys and higher security levels through the use of separate keys for encryption and decryption. Decoupling of keys is enabled by algorithms using random number generation and one - way mathematical functions.

3. Authentication and Non - Repudiation
The use of a codeword or number by the public key holder to verify the identity of the private key holder. For example the bank could have used the number '98765' as their randomly chosen embedded codeword in the encrypted message to me. I then include this in my reply to them. As only my private key could have deciphered this word, this then verifies my identity. The public key encrypts to verify the private key holder. Digital signatures for non - repudiation purposes involves the use of the private key for encryption and decryption by the public key through generation of a hash function:

Hash: SHA1

Your number was 98765 Dear Bank Mgr, Please extend my overdraft. This is my digital signature

Version: PGP 5.5.3
Comment: For Public Key Please Request Via Email

zEhoAnApv /btI28rRpLcw946XNrWzE7AL

The recipient uses my public key to decrypt the received hash function and regenerate it anew in order to match against the original made by the private key.

The main difference between authentication and digital signatures is the functions performed by the private and public keys. The encrypted hash function or digital signature is unique to the private key and cannot be generated in the same way by the public key. For authentication the public key is used for encryption whereas for non - repudiation the private key is used for encryption. For both authentication and non - repudiation the private key holder is verified by the public key holder by key matching, where the private key must be the correct one to match the public key.

Encryption systems are used in online business transactions such as credit card orders, electronic banking and other applications.

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Contents Mathematics Fermat Physics Wordlist Notes Chemistry Quick Facts Reference LINKS