Logic gates
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Logic gates

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Logic gates Logic gates Presentation Transcript

  • Computer Science 101 Logic Gates and Simple Circuits
  • Transistor - Electronic Switch  Collector   Base Switch Emitter   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
  • Moore’s 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.
  • Gates  A gate is an electronic device that takes 0/1 inputs and produces a 0/1 result.
  • NOT Gate  Output Input  Input Low (0v or 0) Output High (+5v or 1)  +5v Input High (+5v or 1) Output Low (0v or 0) Output is opposite of Input NOT Gate Ground A _ A
  • AND Gate  Output is 1 only if • Input-1 is 1 and • Input-2 is 1  +5v Output = Input1 AND Input2 Input-1 AND Gate A Input-2 B Output AB
  • OR Gate  • A is 1 or if • B is 1 +5v  A Output is 1 if Output = A OR B B OR Gate A Output B A+B
  • Boolean Expression  Python Logical operators • AND • OR • NOT and (Python) or (Python) not (Python)  NOT ((x>y) AND ((x=5) OR (y=3))  not((x>y) and ((x==5)or(y==3)))  while (not((x>y) and ((x==5)or(y==3)))) : …
  • 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.
  • 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 …). Don’t have to know how gate is constructed from transistors.
  • 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.
  • Logic Circuit: _ ____ AB+(A+B)B Input Lines for Variables A B
  • Logic Circuit: _ ____ AB+(A+B)B NOT Gate for B A B _ B
  • Logic Circuit: _ ____ AB+(A+B)B _ Subexpression AB _ AB A B _ B
  • Logic Circuit: _ ____ AB+(A+B)B Subexpression A+B _ AB A A+B B _ B
  • Logic Circuit: _ ____ AB+(A+B)B ___ Subexpression A+B _ AB A A+B B _ B ____ A+B
  • Logic Circuit: _ ____ AB+(A+B)B ___ Subexpression (A+B)B _ AB A A+B B _ B ____ A+B ____ (A+B)B
  • Logic Circuit: _ ____ AB+(A+B)B Entire Expression _ AB A A+B B _ B ____ A+B ____ (A+B)B
  • 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.
  • Logic Circuit Boolean Exp _ _ _ AB AB+AB A _ A B _ B _ AB A+B Entire Expression ______ _ _ (AB+AB)(A+B) ______ _ _ AB+AB
  • Simplification Revisited  Once we have the BE for the circuit, perhaps we can simplify. AB AB A B A B AB A B A B A B A A B A BB A B A AA AB BA B
  • Logic Circuit Reduces to: Boolean Exp
  • The Boolean Triangle Boolean Expression Logic Circuit Truth Table
  • The Boolean Triangle Boolean Expression Logic Circuit Truth Table