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From Wikipedia

Address bus

An address bus is a computer bus (a series of lines connecting two or more devices) that is used to specify a physical address. When a processor or DMA-enabled device needs to read or write to a memory location, it specifies that memory location on the address bus (the value to be read or written is sent on the data bus). The width of the address bus determines the amount of memory a system can address. For example, a system with a 32-bit address bus can address 232 (4,294,967,296) memory locations. If each memory address holds one byte, the addressable memory space is 4 GB.


Early processors used a wire for each bit of the address width. For example, a 16-bit address bus had 16 physical wires making up the bus. As the buses became wider, this approach became expensive in terms of the number of chip pins and board traces. Beginning with the Mostek 4096 DRAM, multiplexed addressing became common. In a multiplexed address scheme, the address is sent in two equal parts. This halves the number of address bus signals required to connect to the memory. For example a 32-bit address bus can be implemented by using 16 wires and sending the first half of the memory address, immediately followed by the second half.

Interesting examples

Accessing an individual byte frequently requires reading or writing the full bus width (a word) at once. In these instances the least significant bits of the address bus may not even be implemented - it is instead the responsibility of the controlling device to isolate the individual byte required from the complete word transmitted. This is the case, for instance, with theVESA Local Bus which lacks the two least significant bits, limiting this bus to aligned 32-bit transfers.

Historically, there were also some examples of computers which were only able to address words.

Public address

A public address system (PA system) is an electronic amplification system with a mixer, amplifier and loudspeakers, used to reinforce a sound source, e.g., a person giving a speech, a DJ playing prerecorded music, and distributing the sound throughout a venue or building.

Simple PA systems are often used in small venues such as school auditoriums, churches, and small bars. PA systems with a larger number of speakers are widely used in institutional and commercial buildings, to read announcements or declare states of emergency. Intercom systems, which are often used in schools, also have microphones in each room so that the occupants can reply to the central office.

There is disagreement over when to call these audio systems sound reinforcement systems or PA systems. Some audio engineers distinguish between the two by technology and capability, while others distinguish by intended use, e.g., sound reinforcement systems are for live music, whereas PA systems are for reproduction of speech and recorded music in buildings and institutions. This distinction is important in some regions or markets, while in other regions or markets the terms are interchangeable. In colloquial British English, a PA system installed for public address in a building is sometimes referred to as a Tannoy system after the company of that name now owned by TC Electronic Group.

Small systems

The simplest PA systems consist of a microphone, a modestly-powered mixer amplifier and one or more loudspeakers. Simple PA systems of this type, often providing 50 to 200 watts of power, are often used in small venues such as school auditoriums, churches, and small bars. A sound source such as a CD player or radio may be connected to a PA system so that music can be played through the system.

Public address systems typically consist of input sources, preamplifiers and/or signal routers, amplifiers, control and monitoring equipment, and loudspeakers. Input sources refer to the microphones and CD Players that provide a sound input for the system. These input sources are fed into the preamplifiers and signal routers that determine the zones to which the audio signal is fed. The preamplified signals are then passed into the amplifiers. Depending on a country's regulations these amplifiers will amplify the audio signals to 50V, 70V or 100V speaker line level. Control equipment monitors the amplifiers and speaker lines for faults before it reaches the loudspeakers. This control equipment is also used for separating zones in a PA system. The loudspeaker is used to transduce electrical signals into analog sound signals.

Large systems

Some PA systems have speakers that cover an entire campus of a college or industrial site, or an entire outdoor complex (e.g., an athletic stadium). More than often this PA system will be used as voice alarm system that make announcement during emergency to evacuate the occupants in a building.

Telephone paging systems

Some analog or IP private branch exchange (PBX) telephone systems use a paging facility that acts as a liaison between the telephone and a PA amplifier. In other systems, paging equipment is not built into the telephone system. Instead the system includes a separate paging controller connected to a trunk port of the telephone system. The paging controller is accessed as either a designated directory number or central office line. In many modern systems, the paging function is integrated into the telephone system, and allows announcements to be played over the phone speakers.

Many retailers and offices choose to use the telephone system as the sole access point for the paging system, because the features is integrated. Many schools and other larger institutions are no longer using the large, bulky microphone PA systems and have switched to telephone system paging, as it can be accessed from many different points in the school.

PA over IP

PA over IP refers to PA paging and intercom systems that use an Ethernet or GSM-R network instead of a centralized amplifier to distribute the audio signal to all paging locations in a building or campus. Network-attached amplifiers and intercom units are used to provide the communication function. At the transmission end, a computer application transmits a digital audio stream via the local area network, using audio from the computer's sound card inputs or from stored audio recordings. At the receiving end, specialized intercom modules receive these network transmissions and reproduce the analog audio signal. These are small specialized network appliances addressable by an IP address just like any other computer on the network.

Such systems are inter-connected by the networking infrastructure and thus allow loss less transmission to remote locations across the Internet or a local area or campus network. It is also possible to provide for multiple or relocatable transmission control stations on such a network.

Long line PA

A Long-line public address (LLPA) system is any public address system with a distributed architecture, normally across a wide geographic area. Systems of this type are commonly found in the rail, light rail and metro industries and allow announcements to be triggered from one or several locations to the rest of the network over low bandwidth legacy copper, normally PSTN lines using DSL modems, or media such as optical fiber, or GSM-R, or IP-based networks. Rail systems typically have an interface with a passenger information system (PIS) server, at each station linked to train describers which state the location of rolling stock on the network from sensors on trackside signaling equipment. The PIS system invokes a stored message to be played from a local or remote digital voice announcement system, or a series of message fragments to be assembled in the correct order. For example: //the//13.29//virgin_trains//sleeper_service//from//London_Paddington//to//Penzance//....//will depart from platform//five//this train is formed of //12_carriages//. Messages are routed via an IP network and are played on local amplification equipment. Taken together, the P

Algorithm examples

This article 'Algorithm examples supplementsAlgorithm and Algorithm characterizations.

An example: Algorithm specification of addition m+n

Choice of machine model:

There is no “best�, or “preferred� model. The Turing machine, while considered the standard, is notoriously awkward to use. And different problems seem to require different models to study them. Many researchers have observed these problems, for example:

“The principal purpose of this paper is to offer a theory which is closely related to Turing's but is more economical in the basic operations� (Wang (1954) p. 63)
“Certain features of Turing machines have induced later workers to propose alternative devices as embodiments of what is to be meant by effective computability.... a Turing machine has a certain opacity, its workings are known rather than seen. Further a Turing machine is inflexible ... a Turing machine is slow in (hypothetical) operation and, usually complicated. This makes it rather hard to design it, and even harder to investigate such matters as time or storage optimization or a comparison between efficiency of two algorithms.� (Melzak (1961) p. 281)
Shepherdson-Sturgis (1963) proposed their register-machine model because “these proofs [using Turing machines] are complicated and tedious to follow for two reasons: (1) A Turing machine has only one head... (2) It has only one tape....� They were in search of “a form of idealized computer which is sufficiently flexible for one to be able to convert an intuitive computational procedure into a program for such a machine� (p. 218).
“I would prefer something along the lines of the random access computers of Angluin and Valiant [as opposed to the pointer machine of Schönhage]� (Gurivich 1988 p. 6)
“Showing that a function is Turing computable directly...is rather laborious ... we introduce an ostensibly more flexible kind of idealized machine, an abacus machine...� (Boolos-Burgess-Jeffrey 2002 p.45).

About all that one can insist upon is that the algorithm-writer specify in exacting detail (i) the machine model to be used and (ii) its instruction set.

Atomization of the instruction set:

The Turing machine model is primitive, but not as primitive as it can be. As noted in the above quotes this is a source of concern when studying complexity and equivalence of algorithms. Although the observations quoted below concern the Random access machine model – a Turing-machine equivalent – the problem remains for any Turing-equivalent model:

“...there hardly exists such a thing as an ‘innocent’ extension of the standard RAM model in the uniform time measure; either one only has additive arithmetic, or one might as well include all multiplicative and/or bitwise Boolean instructions on small operands....� (van Emde Boas (1992) p. 26)
“Since, however, the computational power of a RAM model seems to depend rather sensitively on the scope of its instruction set, we nevertheless will have to go into detail...
“One important principle will be to admit only such instructions which can be said to be of an atomistic nature. We will describe two versions of the so-called successor RAM, with the successor function as the only arithmetic operation....the RAM0 version deserves special attention for its extreme simplicity; its instruction set consists of only a few one letter codes, without any (explicit) addressing.� (Schönhage (1980) p.494)

Example #1: The most general (and original) Turing machine – single-tape with left-end, multi-symbols, 5-tuple instruction format – can be atomized into the Turing machine of Boolos-Burgess-Jeffrey (2002) – single-tape with no ends, two "symbols" { B, | } (where B symbolizes "blank square" and | symbolizes "marked square"), and a 4-tuple instruction format. This model in turn can be further atomized into a Post-Turing machine– single-tape with no ends, two symbols { B, | }, and a 0- and 1-parameter instruction set ( e.g. { Left, Right, Mark, Erase, Jump-if-marked to instruction xxx, Jump-if-blank to instruction xxx, Halt } ).

Example #2: The RASP can be reduced to a RAM by moving its instructions off the tape and (perhaps with translation) into its finite-state machine “table� of instructions, the RAM stripped of its indirect instruction and reduced to a 2- and 3-operand “abacus� register machine; the abacus in turn can be reduced to the 1- and 2-operand Minsky (1967)/Shepherdson-Sturgis (1963) counter machine, which can be further atomized into the 0- and 1-operand instructions of Schönhage (and even a 0-operand Schönhage-like instruction set is possible).

Cost of atomization:

Atomization comes at a (usually severe) cost: while the resulting instructions may be “simpler�, atomization (usually) creates more instructions and the need for more computational steps. As shown in the following example the increase in computation steps may be significant (i.e. orders of magnitude – the following example is “tame�), and atomization may (but not always, as in the case of the Post-Turing model) reduce the usability and readability of “the machine code�. For more see Turing tarpit.

Example: The single register machine instruction "INC 3" – increment the contents of register #3, i.e. increase its count by 1 – can be atomized into the 0-parameter instruction set of Schönhage, but with the equivalent number of steps to accomplish the task increasing to 7; this number is directly related to the register number “n� i.e. 4+n):

More examples can be found at the pages Register machine and Random access machine where the addition of "convenience instructions" CLR h and COPY h1,h1 are shown to reduce the number of steps dramatically. Indirect addressing is the other significant example.

Precise specification of Turing-machine algorithm m+n

As described in Algorithm characterizations per the specifications of Boolos-Burgess-Jeffrey (2002) and Sipser (2006), and with a nod to the other characterizations we proceed to specify:

(i) Number format: unary strings of marked squares (a "marked square" signfied by the symbol 1) separated by single blanks (signified by the symbol B) e.g. “2,3� = B11B111B
(ii) Machine type: Turing machine: single-tape left-ended or no-ended, 2-symbol { B, 1 }, 4-tuple instruction format.
(iii) Head location: See more at “Implementation Description� below. A symbolic representation of the head's location in the tape's symbol string will put the current state to the right of the scanned symbol. Blank squares may be included in this protocol. The state's number will appear with brackets around it, or sub-scripted. The head is shown as

From Yahoo Answers

Question:I'm trying to get a shipment online from Amazon and I don't know how this works because I never ordered anything before..anyway there's this 2 lines which has Address line 1 and 2. For the first one it said (Street address, P.O. box, company name, c/o ) as for the second one it is (Apartment, suite, unit, building, floor, etc.) so can you please explain to me what each one means with an example and btw I live in a apartment...and I would like to know how and where to fill out on the shipping and payment. Thanks.

Answers:They do that in case you have a two line address. For an apartment, your apartment number would go on the Address 2 line like so: Address 1: 123 Main Street Address 2: Apartment A-12

Question:Hello, I'm to receive a MasterCard via regular mail, they asked me to provide: Street Address Line 1 (limit to 30 characters): Street Address Line 2 (limit to 30 characters): City/State: Country: Zip Code: So, what are line 1 and line 2? which one contains building number? buildings-group name, apartment number, street, etc.? Please provide a simple example. Thank you!

Answers:It's typically best to put the apartment number on line 2 if you have one. This is because some companies printing mail only have a certain number of characters; if the apartment number is on line one it may get cut off and mail might not reach you. Example: 100 Main St. Apt 111


Answers:address line 1: your full, legal name (i.e. John Smith) address line 2: your street address (i.e. 123 Main Street) address line 3: any address specifics (optional) (i.e. Suite #100 or Second Floor, etc.) address line 4: city, state and zip (i.e. Beverly Hills, CA 90210)

Question:So, when you go to fill out the billing information, and it requires an Address, what's the difference between Address Line 1 and 2? So if I live in a regular house under number 13, I write my street and number to Address line 1?

Answers:Line 2 is for like an apartment or unit number. Line 1 is your actual street address

From Youtube

Line Integral Example 1 :Concrete example using a line integral