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# Computer Science 101 - PowerPoint PPT Presentation

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. I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
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Presentation Transcript ### 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.
• What value each output should have for each setting of the inputs. 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
• 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
• Find Boolean expression for the output.
• Note that this is a “Majority Rules” circuit.
• The output reflects the majority input. 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
• 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
• 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
• Want BE that is true if
• _ ABC is true OR
• _ ABC is true OR
• _ ABC is true
• _ _ _ ABC+ABC+ABC 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
• 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
• 1’s in output give _ _ _ _ABC + ABC _ _+ ABC + ABC A

B

C

_ _ _ _ _ _

ABC+ABC+ABC+ABC

Boolean Expression

Circuit for the example 