2-the needs of computation

7/30/2019 2-The Needs of Computation

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2013/5/23 COPYRIGHT [email protected] 1

Unit II: The Needs of Computation


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Humans Everyday Life

Eating, working, sleeping,

The Human Beings

Eat less than pigs

Are weaker than apes and elephants

Run slower than panthers

However, the human beings are intelligent

Trying to do many things that we have to do or

we are not able to do More more, bigger, larger, faster, longer,

In short, we solve various problems in everyday life


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Humans Problem-Solving

Problem solving is a sequence of steps or methods thatsolve part of the domain problem

Physically or Mechanically

To run faster: bicycles, cars, trains, To make more food: toaster, mills,

To fly high: aircrafts, jets,

Machines are stronger, faster, more accurate than thehuman beings and they never get tired.

To design machines that implement the sequence of steps ofproblem-solving


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Humans Problem-Solving

Problem solving is a sequence of steps ormethods that solve part of the domain problem

To improve the ability of human mind

To read, to write, to teach, to learn, even to think

What is the sequence of steps or methods to realizereading (writing, teaching, learning, or thinking)?

Mathematics is the one (close but not perfect)


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Computing, Computation, and

Computers

Problem-solving

HumanMachineMathematics

Mathematics problem-solving

Numbers/Symbols

Calculation Steps

For computing

The computing machine (or computer)

The main task is to compute


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The difference between humans and

computing machines

In human beings

input

think

act


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The difference between humans and

computing machines In machines

input

compute

act


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Transformation

input

think

act

input

compute

act


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Transformation

Transformation Representation (I/P)

Interfacing Sensing (e.g., DSP) Data structure etc.

Representation (O/P) Control Robotics Mechanism

etc.


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Transformation

Humans problem-solving strategies

Mathematical representation/reasoning

Machine executable steps

Algorithm Design Programming Language

Data structure + Algorithm = Program

Program + Computer

Computer-based problem-solvingHuman problem-solving

think

compute


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Representation of the World

Calendar

Month: 12, Week: 7, Day: 30

Hour: 12/24, Min./Sec.: 60

others Number Systems in Humans Life

7, 10, 12, 24, 60

How to compute in these number

systems?


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Computation in Different Number

Systems

Math.

10

Computing in the 10-based number system

Human: +

Machine:

Some ways to represent 10 different states

Physical limitations and constraints What materials?

Cost/Performance/Capacity?


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Design Issues

A Machine that is capable of

representing N-based number system (N different

states)

performing fast and accurate computation in the N-based number system

being reliable and not too expensive

Binary system is the oneWhy?


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The Binary System

The binary system There are only 2 different states

ON/OFF, B/W, 1/0, etc.

To represent the world using binary notations

Data represented in other number systems have to be

transformed into the binary system Computation is done in the binary system

The result is converted from its binary format into the originalformat

;;;;

(20 212223242526)


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The Binary System

Computation in the 10-based number system5+3=8

1000*25=25000

Computation in the binary number systemHow to ?

Algebra? Operator? Operand?

ON + ON * OFF = ??

Performing a sequence of binary operations


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The Binary Computing System

Computer: A computing mechanism that performs

binary operations

Currently, they are implemented in silicon chips (VLSI)

Circuits for computation

01111

0001110010

15

3+10 +2 18


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Problem-solving using computers

Computers solve computable problems

A Problem

Describing

The Problem

in Math.

ComputingThe

Corresponding

Math.

Problem

Returning

The Result

Solution

To The

Problem

Human problem-solving v.s. computer-based problem-solving


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Conclusion

Computers are for human problem-solving

Mathematical representation of problems and solvingsteps

Computers are computing machines Computers solve computable problems

Some problems are un-computable

Current computers are implemented in the binary

numeric system (due to the limitations of physicalimplementation)

2-the needs of computation

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