Computer Science 101

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Computer Science 101

• Logic Gates and Simple Circuits

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Transistor - Electronic Switch

• Base High (5v or 1) Makes connection
• Base Low (0v or 0) Disconnects
• Say, 500 million transistors on a chip 1 cm2
• Change states in billionth of sec
• Solid state

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Moores Law
In 1965, Intel co-founder Gordon Moore saw the
future. His prediction, now popularly known as
Moore's Law, states that the number of
transistors on a chip doubles about every two
years.
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Gates

• A gate is an electronic device that takes 0/1
  inputs and produces a 0/1 result.

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NOT Gate

• Input High (5v or 1) Output Low (0v or 0)
• Input Low (0v or 0) Output High (5v or 1)
• Output is opposite of Input

5v
Output
Input
Ground
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AND Gate
5v

• Output is 1 only if
• Input-1 is 1 and
• Input-2 is 1
• Output Input1 AND Input2

Output
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OR Gate

• Output is 1 if
• A is 1 or if
• B is 1
• Output A OR B

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Boolean Expression ? Python

• Logical operators
• AND ? and (Python)
• OR ? or (Python)
• NOT ? not (Python)
• NOT ((xgty) AND ((x5) OR (y3))
• not((xgty) and ((x5)or(y3)))
• while (not((xgty) and ((x5)or(y3))))

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Abstraction

• In computer science, the term abstraction refers
  to the practice of defining and using objects or
  systems based on the high level functions they
  provide.
• We suppress the fine details of how these
  functions are carried out or implemented.
• In this way, we are able to focus on the big
  picture.
• If the implementation changes, our high level
  work is not affected.

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Abstraction Examples

• Boolean algebra - we can work with the Boolean
  expressions knowing only the properties or laws -
  we do not need to know the details of what the
  variables represent.
• Gates - we can work with the logic gates knowing
  only their function (output is 1 only if inputs
  are ). Dont have to know how gate is
  constructed from transistors.

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Boolean Exp ? Logic Circuit

• To draw a circuit from a Boolean expression
• From the left, make an input line for each
  variable.
• Next, put a NOT gate in for each variable that
  appears negated in the expression.
• Still working from left to right, build up
  circuits for the subexpressions, from simple to
  complex.

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Logic Circuit _ ____ AB(AB)B
Input Lines for Variables
A
B
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Logic Circuit _ ____ AB(AB)B
NOT Gate for B
A
B
_ B
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Logic Circuit _ ____ AB(AB)B
_ Subexpression AB
_ AB
A
B
_ B
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Logic Circuit _ ____ AB(AB)B
Subexpression AB
_ AB
A
AB
B
_ B
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Logic Circuit _ ____ AB(AB)B
___ Subexpression AB
_ AB
A
____ AB
AB
B
_ B
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Logic Circuit _ ____ AB(AB)B
___ Subexpression (AB)B
_ AB
A
____ AB
AB
B
_ B
____ (AB)B
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Logic Circuit _ ____ AB(AB)B
Entire Expression
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Logic Circuit ? Boolean Exp

• In the opposite direction, given a logic circuit,
  we can write a Boolean expression for the
  circuit.
• First we label each input line as a variable.
• Then we move from the inputs labeling the outputs
  from the gates.
• As soon as the input lines to a gate are labeled,
  we can label the output line.
• The label on the circuit output is the result.

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Logic Circuit ? Boolean Exp
_ _ ABAB
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Simplification Revisited

• Once we have the BE for the circuit, perhaps we
  can simplify.

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Logic Circuit ? Boolean Exp
Reduces to
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The Boolean Triangle
Boolean Expression
Logic Circuit
Truth Table
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The Boolean Triangle
Boolean Expression
Logic Circuit
Truth Table
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If we only had an Al Gore Rhythm!