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Computer Science 101 . Circuit Design Algorithm. Circuit Design - The Problem. The problem is to design a circuit that accomplishes a specified task. What does this mean? What kind of task? We would like to specify The number of inputs to the circuit. The number of outputs.

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computer science 101

Computer Science 101

Circuit Design Algorithm

circuit design the problem
Circuit Design - The Problem
  • The problem is to design a circuit that accomplishes a specified task.
  • What does this mean?
  • What kind of task?
  • We would like to specify
    • The number of inputs to the circuit.
    • The number of outputs.
    • What value each output should have for each setting of the inputs.
circuit design observations
Circuit Design - Observations
  • We can deal with one output at a time.
  • The truth table is a good way to organize the specifications.
  • If we can come up with a Boolean expression for the output, we’re home free.
circuit design and truth table
Circuit Design and Truth Table
  • The problem reduces to this:
    • Given a truth table with all values for inputs.
    • And given a column of values for the output.
    • Find a Boolean expression that yields the specified column.
  • If we can do this, we can get the circuit from the Boolean expression.
  • We now develop an algorithm, the Sum of Products algorithm, to find the expression.
circuit design typical problem
Circuit Design - Typical Problem
  • Find Boolean expression for the output.
  • Note that this is a “Majority Rules” circuit.
  • The output reflects the majority input.
circuit design first case
Circuit Design - First Case
  • Consider case where output column has only one 1.
  • Want expression which is true when
    • A is false _ (A true) and
    • B is true and
    • C is true
  • _ ABC does the trick.
sum of products algorithm single 1
Sum of Products Algorithm- Single 1
  • Note row in which the 1 occurs.
  • Make a product of all the input variables.
  • Put a bar over each variable that has a value of 0 in this row.
sum of products single 1
Sum of Products - Single 1
  • Note row where the 1 occurs.
  • Make product of all variables. ABC
  • Put bar over variables with 0 value. _ ABC
sum of products general case
Sum of Products - General Case
  • Want BE that is true if
    • _ ABC is true OR
    • _ ABC is true OR
    • _ ABC is true
  • _ _ _ ABC+ABC+ABC
sum of products algorithm
Sum of Products Algorithm
  • Identify each row of the output that has a 1.
  • For each such row
    • Make a product of all the input variables.
    • Put bar over each variable with a 0 in this row.
  • Make a sum of all of these product terms.
sum of products example
Sum of Products - Example
  • Problem: Design a logic circuit with
    • 3 input lines, 1 output line
    • Anytime we change the value of any one of the inputs, the output value changes.
    • Think of a single light bulb controlled by three light switches that work independently.
  • Note: Once we set the output for one set of inputs, the rest is determined.
  • We’ll start with all inputs 0 giving output 0.
example continued
Example continued
  • 1’s in output give _ _ _ _ABC + ABC _ _+ ABC + ABC
circuit for the example

A

B

C

_ _ _ _ _ _

ABC+ABC+ABC+ABC

Boolean Expression

Circuit for the example