Gates and Circuits

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Gates and Circuits
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Three Main Gates

• AND
• OR
• NOT

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NAND Gates

• NOT AND

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Gate Diagrams

• Example MR S

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Gate Diagrams

• Example

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Gate Diagrams

• Example (MR S) (RS)

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Gate Diagrams

• Exercise

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Truth Table (to Expression) to Gates

• First, build the Boolean algebra expression that
  gives Z
• Z AB AB

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Truth Table to Gates

• Z AB AB
• Next, build the circuit that goes with the
  Boolean algebra expression Z

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Z AB AB
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Boolean Expression to Gates

• Exercise
• (A B) A

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Boolean Expression to Gates

• Exercise
• (A B) A

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Multi-input AND and OR

• What circuit corresponds to ABC?
• ABC?

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Binary Addition

• The first step in building our computer

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Binary Addition
Sum
Carry
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Binary Addition

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Sum Circuit

Sum AB AB
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Carry Circuit
Carry AB
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Half Adder - Sum and Carry
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Full Adder

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4 Bit Adder

• Computers represent numbers in parallel.

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Exercises

• Give Boolean expressions and construct circuits
  with the following properties (using AND, OR or
  NOT gates)

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Exercises

• A) B)?

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Exercises

• 2 - Fill in a truth table and give a Boolean
  expression for the following circuit.