the needs of computation

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Unit II: The Needs of Computation

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Human’s 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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Human’s Problem-Solving

• Problem solving is a sequence of steps or methods that solve 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 the human beings and they never get tired. – To design machines that implement the sequence of steps of

problem-solving

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Human’s Problem-Solving

• Problem solving is a sequence of steps or methods 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 realize

reading (writing, teaching, learning, or thinking)?

• Mathematics is the one (close but not perfect)

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Computing, Computation, and Computers

• Problem-solving – Human Machine Mathematics

• 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• Human’s problem-solving strategies

Mathematical representation/reasoning

Machine executable steps– Algorithm Design

– Programming Language

• Data structure + Algorithm = Program• Program + Computer

Computer-based problem-solving Human 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 Human’s 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 one– Why?

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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 original for

mat• 易經

– 易有太極 ; 太極生兩儀 ; 兩儀生四象 ; 四象生八卦 ; 八卦生六十四爻 – (20 21 22 23 24 25 26 …)

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The Binary System• Computation in the 10-based number system

– 5+3=8– 1000*25=25000

• Computation in the binary number system– How 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 ProblemA ProblemDescribing

The Problemin Math.

Describing The Problem

in Math.

“Computing”The

CorrespondingMath.

Problem

“Computing”The

CorrespondingMath.

Problem

ReturningThe Result

ReturningThe Result

Solution To The Problem

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 solving

steps• 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 physical implementation)