the needs of computation
TRANSCRIPT
112/04/12 COPYRIGHT [email protected] 2
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
112/04/12 COPYRIGHT [email protected] 3
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
112/04/12 COPYRIGHT [email protected] 4
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)
112/04/12 COPYRIGHT [email protected] 5
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”
112/04/12 COPYRIGHT [email protected] 6
The difference between humans and computing machines
• In human beings
input
think
act
112/04/12 COPYRIGHT [email protected] 7
The difference between humans and computing machines
• In machines
input
compute
act
112/04/12 COPYRIGHT [email protected] 9
Transformation
Transformation Representation (I/P)
Interfacing Sensing (e.g., DSP) Data structure etc.
Representation (O/P) Control Robotics Mechanism etc.
112/04/12 COPYRIGHT [email protected] 10
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
112/04/12 COPYRIGHT [email protected] 11
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?
112/04/12 COPYRIGHT [email protected] 12
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?
112/04/12 COPYRIGHT [email protected] 13
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?
112/04/12 COPYRIGHT [email protected] 14
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 …)
112/04/12 COPYRIGHT [email protected] 15
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
112/04/12 COPYRIGHT [email protected] 16
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
112/04/12 COPYRIGHT [email protected] 17
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
112/04/12 COPYRIGHT [email protected] 18
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)