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Basic Digital Logic:AND, OR and NOT gates

©Paul GodinCreated August 2007

Last Update Sept 2013

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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.

Input Output

0 0 0

0 1 1

1 0 1

1 1 1

Every possible input combination

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Basic Digital Logic Functions

Digital logic is based on 3 primary functions (the Basic Gates):

AND

OR

NOT

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The AND Operation

ANDAll 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”

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AND Logic Symbol

Inputs Output

If all inputs are 1, the output is 1

If any input is 0, the output is 0

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AND Logic Symbol

Inputs Output

Determine the output

0

0

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AND Logic Symbol

Inputs Output

Determine the output

0

1

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AND Logic Symbol

Inputs Output

Determine the output

1

1

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AND Truth Table

Input Output

0 0 0

0 1 0

1 0 0

1 1 1

AND

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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 = xAB = x

&

The AND operation operates similarly to multiplication.

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The OR Operation

ORIf 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”

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OR Logic Symbol

Inputs Output

If any input is 1, the output is 1

If all inputs are 0, the output is 0

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OR Logic Symbol

Inputs Output

Determine the output

0

0

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OR Logic Symbol

Inputs Output

Determine the output

0

1

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OR Logic Symbol

Inputs Output

Determine the output

1

1

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OR Truth Table

Input Output

0 0 0

0 1 1

1 0 1

1 1 1

OR

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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

◊ Boolean equation for an OR gate:A+B = x

≥1

The OR operation operates similarly to Addition.

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The NOT Operation

NOTThe 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 or COMPLIMENTARY.

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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 Output

Determine the output

0

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NOT Logic Symbol

Input Output

Determine the output

1

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NOT Truth Table

Input Output

0 1

1 0

NOT

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NOT Gates

◊ IEEE symbol for a NOT gate:

◊ Boolean for a NOT function:A = x (overbar symbol)A’ = x (prime symbol)

1

Note: The triangle symbol on the output is considered the NOT function

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Alternate Symbols

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

◊ Alternate symbols for the NOT gate:

1

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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

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Review 2

AND Logic Symbol

OR Logic Symbol

NOT (or Inverter) Logic Symbol

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Review 3

A ● B = Y AB = Y

A + B = Y

A = YA’ = Y

A AND B = Y

A OR B = Y

NOT A = Y

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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 tablesInput Output

0 0

0 1

1 0

1 1

≥1

Input Output

0 0

0 1

1 0

1 1

&

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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)

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End

©Paul R. Godinprgodin°@ gmail.com