Basic Digital Logic: AND, OR and NOT gates

©Paul Godin Basic Gates 1.1

Last Update Sept 2013

Digital Logic: Introduction

◊ The foundation of digital systems is the ability to make logic-based decisions on input states.

◊ Boolean Algebra is a relatively simple mathematic form based on logic functions comprising of two states: true (logic 1) or false (logic 0). It is used to describe output states based on a set of input states.

◊ Boolean mathematics has been around for over a hundred years but much of it is well suited to digital systems. Boolean logic is used in internet search engines.

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Truth Tables

Truth tables describe the function of a digital device. They show the output states based on input states.

Every possible input combination 0 1 0 Input 0 1 1 1 0 Output 0 1 1 1 Basic Gates 1.3

Basic Digital Logic Functions

Digital logic is based on 3 primary functions (the Basic Gates): AND OR NOT Basic Gates 1.4

The AND Operation AND All inputs must be True for the output to be True.

◊ Other ways to describe AND : ◊ ◊ ◊ If all inputs are 1 the output is 1 If any input is 0, the output is 0 “If this input AND this input are 1, the output is 1” Basic Gates 1.5

AND Logic Symbol

Inputs Output If all inputs are 1, the output is 1 If any input is 0, the output is 0 Basic Gates 1.6

AND Logic Symbol

Inputs

0 0

Determine the output Output Basic Gates 1.7

AND Logic Symbol

Inputs

0 1

Determine the output Output Basic Gates 1.8

AND Logic Symbol

Inputs

1 1

Determine the output Output Basic Gates 1.9

AND Truth Table

0 1 0 Input 0 1 1 1 0

AND

Output 0 0 0 1 Basic Gates 1.10

AND Gates

It is possible to have AND gates with more than 2 inputs. The same logic rule applies – all inputs must be 1 for the output to be 1.

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AND Gates

◊ IEEE symbol for an AND gate & ◊ Boolean equations for an AND gate: A●B = x AB = x The AND operation operates similarly to multiplication. Basic Gates 1.12

The OR Operation OR

If any input is True, the output is True Other ways to describe OR : ◊ if any input is 1, the output is 1 ◊ ◊ if all inputs are 0, the output is 0 “If this input OR this input is 1, the output is 1” Basic Gates 1.13

OR Logic Symbol

Inputs Output If any input is 1, the output is 1 If all inputs are 0, the output is 0 Basic Gates 1.14

OR Logic Symbol

Inputs

0 0

Determine the output Output Basic Gates 1.15

OR Logic Symbol

Inputs

0 1

Determine the output Output Basic Gates 1.16

OR Logic Symbol

Inputs

1 1

Determine the output Output Basic Gates 1.17

OR Truth Table

1 1 0 Input 0 0 1 0 1

OR

Output 0 1 1 1 Basic Gates 1.18

OR Gates

It is possible to have OR gates with more than 2 inputs. The same logic rule applies – If any input is 1, the output is 1.

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OR Gates

◊ IEEE symbol for an OR gate ≥1 ◊ Boolean equation for an OR gate: A+B = x The OR operation operates similarly to Addition.

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The NOT Operation NOT

The output is the opposite state of the input.

◊ Other ways to describe NOT : ◊ If any input is 1, the output is 0 ◊ If any input is 0, the output is 1 The NOT function is often called INVERTER COMPLIMENTARY .

or Basic Gates 1.21

NOT Logic Symbol

Input Output If the input is 1, the output is 0 If the input is 0, the output is 1 Note: The “bubble” on the output is considered the NOT function.

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NOT Logic Symbol

Input

0

Determine the output Output Basic Gates 1.23

NOT Logic Symbol

Input

1

Determine the output Output Basic Gates 1.24

NOT Truth Table

Input 0 1

NOT

Output 1 0 Basic Gates 1.25

NOT Gates

◊ IEEE symbol for a NOT gate: 1 ◊ Boolean for a NOT function: A = x (overbar symbol) A’ = x (prime symbol) Note: The triangle symbol on the output is considered the NOT function Basic Gates 1.26

Alternate Symbols

◊ The NOT is the “bubble” on the gate.

◊ Alternate symbols for the NOT gate: 1 Basic Gates 1.27

Review 1

◊ There are 3 basic gates: ◊ AND, where all inputs must be high for a high output ◊ OR, where any input must be high for a high output ◊ NOT, where the output is the opposite (compliment) of the input Basic Gates 1.28

Review 2

AND Logic Symbol OR Logic Symbol NOT (or Inverter) Logic Symbol Basic Gates 1.29

Review 3

A ● B = Y AB = Y A AND B = Y A + B = Y A OR B = Y A = Y A’ = Y NOT A = Y Basic Gates 1.30

Exercise 1

What is the outcome of the following:

1 1 0 1 0 1 1

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Exercise 2

Complete the sentences: ◊ If all inputs of an OR gate are low, the output is_________ ◊ If any input of an AND gate is low, the output is _________ ◊ The output of a NOT gate is always the ___________ of the input.

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Exercise 3

Complete the tables ≥1 &

Input 0 0 1 1 0 1 0 1 Output Input 0 0 1 1 0 1 0 1 Output

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Exercise 4

Draw the logic equivalent of the AND and the OR gates using switches.

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Exercise 5

A vehicle has 2 proximity sensors and one motor. When triggered, the sensors produce a logic 1. The motor goes forward with a logic 0 and stops with a logic 1.

If both sensors sense an object, stop. If only one, or none of the sensors sense an object, go forward.

Draw the sensors, motor and the logic needed. (Hint: do a truth table) Basic Gates 1.35

End

©Paul R. Godin prgodin

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@ gmail.com

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