basic digital logic 1
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Basic Digital Logic 1Basic Gates
Paul Godin
January 2004
Created for the Western Canadian Robotics Society
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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
Determine the output
Animated Slide
0
1 0
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AND Logic Symbol
Inputs Output
Determine the 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
Determine the output
Animated Slide
0
0 0
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OR Logic Symbol
Inputs Output
Determine the output
Animated Slide
0
1 1
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OR Logic Symbol
Inputs Output
Determine the 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
Determine the output
Animated Slide
0 1
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NOT Logic Symbol
InputOutput
Determine the output
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]