Basic Digital Logic 1

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Basic Digital Logic 1Basic Gates

Paul Godin

[email protected]

January 2004

Created for the Western Canadian Robotics Society
mailto:[email protected]:[email protected]


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Basic Digital Logic 1

This presentation is about the basicconcepts of Digital Electronics:

Basic Logic Concepts Basic Logic Functions

Logic Symbols

Truth Tables


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Basic Digital Logic 1

Basic Logic Concepts


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Digital Signals

Digital Signals have two basic states:

1 (logic high, or H, or on)

0 (logic low, or L, or off)

Digital values are in a binaryformat.Binary means 2 states.

A good example of binary is a light(only on or off)


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Binary

Base 2 = Base 10

000 = 0

001 = 1

010 = 2

011 = 3

100 = 4101 = 5

110 = 6

111 = 7

In Binary, there are only 0s and 1s. These

numbers are called Base-2( Example: 0102)

Binary

toDecimal

We count in Base-10(0 to 9)


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Binary as a Voltage

Voltages are used to represent logic values:

A voltage present (called Vcc or Vdd) = 1

Zero Volts or ground (called gnd or Vss) = 0

A simple switch can provide a logic high or a logic low.


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A Simple Switch

Here is a simple switch used toprovide a logic value:

Vcc

Gnd, or 0

Vcc

Vcc, or 1

There are other ways to connect a switch.


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Digital Logic

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

AND

OR

NOT


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The AND function

The AND function:

If all the inputs are high is the output ishigh

If any input is low, the output is low

If this input AND this input are

high, the output is high


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AND Logic Symbol

InputsOutput

If both 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

Animated Slide

0

0 0


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AND Logic Symbol

Inputs Output


Animated Slide

0

1 0


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AND Logic Symbol

Inputs Output


Animated Slide

1

1 1


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AND Truth Table

To help understand the function of adigital device, a Truth Table is used:

Input Output0 0 0

0 1 0

1 0 01 1 1

AND Function

Every possibleinput combination


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AND Gates

It is possible to have AND gateswith more than 2 inputs. The samelogic rules apply if any input


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The OR function

The OR function:

if any input is high, the output is high

if all inputs are low, the output is low

If this input OR this input is high,the output is high


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OR Logic Symbol

InputsOutput

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


Animated Slide

0

0 0


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OR Logic Symbol

Inputs Output


Animated Slide

0

1 1


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OR Logic Symbol

Inputs Output


Animated Slide

1

1 1


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OR Truth Table

Truth Table

Input Output0 0 0

0 1 1

1 0 1

1 1 1

OR Function


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The NOT function

The NOT function:

If any input is high, the output is low

If any input is low, the output is high

The output is the opposite state ofthe input

The NOT function is often calledINVERTER


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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


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NOT Logic Symbol

InputOutput


Animated Slide

0 1


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NOT Logic Symbol

InputOutput


Animated Slide

1 0


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NOT Truth Table

Truth Table

Input Output0 1

1 0

NOT Function


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REVIEW

Digital Electronics works in Binary:

There are 2 logic levels: high and low,or 1 and 0.

A switch can be used to provide a logiclevel.


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REVIEW

There are 3 basic gates:

AND, where all inputs must be high fora high output

OR, where any input must be high foran output high

NOT, where the output is the opposite(compliment) of the input


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Exercise 1

1. Least Challenging

Complete the sentences:

If all inputs of an OR gate are low, theoutput is_________

If any input of an AND gate is low, theoutput is _________

The output of a NOT gate is always the___________ of the input.


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Exercise 2

2. A bit challenging:

Convert the binary numbers to theirbase-10 value:

0102= ___10

01102=____10

10012 = ____10


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Exercise 3

3. Challenging

A robot has a motor that:

goes forward when it gets a logic 1

stops when it gets a logic 0

There is a touch sensor switch at thefront of the robot.

Draw a diagram of the sensor switchand the connection to the motor.


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Exercise 4

4. More Challenging A robot has two touch sensors and one

motor. When pushed, the sensors

produce a logic 1. The motor goesforward with a logic 0 and backwardwith a logic 1.

If both sensors sense a touch, gobackward. If only one, or none of the

sensors sense a touch, go forward. Draw the sensors, motor and the logic

needed. (Hint: do a truth table)


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Exercise 5

5. Expert Level A robot has three touch sensors (left, right,

middle). When pushed, they produce a logic 0.

The robot has two motors (left and right). Alogic 1 will make them go forward and a logic 0will make them go backward.

See the next slide for the desired operation.Design your circuit using switches, logic gatesand motors.


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Exercise 5

Inputs Outputs

L C R L R

0 0 0 0 0

0 0 1 0 1

0 1 0 1 1

0 1 1 1 1

1 0 0 1 0

1 0 1 1 1

1 1 0 1 1

1 1 1 1 1

5. Continued


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End of Basic Digital Logic 1

Copyright WCRS and Paul GodinFor non-profit use only
mailto:[email protected]:[email protected]:[email protected]:[email protected]

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Basic Digital Logic 1