Transcript by Justin Champion - Staffordshire University

Computer Logic &
Logic Gates
Justin Champion
IITCT

Contents
Introduction to Logic
 Look at the different Logic Gates
 Summary

IITCT - Logic
George Boole
1815 to 1864
Boole approached logic in a new way reducing it to a simple
algebra, incorporating logic into mathematics. He also worked
on differential equations, the calculus of finite differences and
general methods in probability.
IITCT - Logic

Boolean Logic

Something is either
•
•
•

True or False
1 or 0
Correct or Wrong
Computers use this to make decisions
•
A computer is basically a large number of switches
•

Each of these can be either in the state of on (1) or off (0)
We do use this kind of logic every single day
IITCT

You can only get into the night club if you have a coloured
suit
True
Get into Club
False
Refused Entry to Club
IITCT

Logic

As seen you use this all the time
•
If (suit coloured) then
•
•
Else
•


Entry to club
Refused Entry
You can also put multiple conditions together
Conditional Logic
•
If (Suit Coloured and hat on the head) then
•
•
Entry to club
Else
•
Refused Entry
IITCT

You can only get into the club if you have a coloured suit
and a hat on your head!
False
True
Refused Accepted
False
Refused
False
Refused
IITCT

All of the previous are examples of Boolean Logic

Basic Logic Conditions Available
•
•
•

AND
OR
NOT
Logic Symbols used in diagrams
•
•
•
AND
OR
NOT
.
+
IITCT

Use of The Logic Symbols




If person wearing a Jacket AND a tie then enter
Entry = Jacket.Tie
If person wearing a jacket which is NOT white AND a tie
then enter
Entry = (jacket.white).tie
IITCT

What you have seen is every day examples of Logic


This is exactly what is used inside of computers to make
decisions
The following section will look at the formal method
describing truth tables
•
•
This is no more complicated than the previous examples
It is just a matter of realising this fact
IITCT

Switches


To represent the logic of 1 and 0 we use switches which
turn off (0) and on (1)
These switches are referred to as transistors
Collector
Collector
Base
Base
Flow
No Flow
1 Volt
0 Volts
Emitter
Emitter
IITCT

Processors use large numbers of these transistors to
make decisions

AMD 3200+ processor has 54.3 Million transistors!
IITCT

Example Truth Tables
A
B
A.B A+B A
A+B
0
0
0
0
1
1
0
1
0
1
1
0
1
1
1
1
0
0
1
0
0
1
0
0
AND
OR
NOT
NOT (A or B)
IITCT

To create a truth table first of all list all of the conditions

For binary values the number of unique conditions will be
•
•
•
2 number of conditions
So for this example it will 22 giving 4 unique conditions
For 3 conditions it will be 23 giving 8 unique conditions
A
B
0
0
0
1
1
1
1
0
IITCT

Try a truth table yourself

Create a truth table for
•
If man has long hair and not a member entry refused
IITCT

Answer

Create a truth table for
•
If person has long hair and not a member entry refused
Long Hair Member Not Member
0
0
1
1
1
0
1
0
0
1
0
1
Long Hair.Member
Accepted
Accepted
Accepted
Refused
IITCT

What this logic looks like in electrical circuits

First the truth table
A
0
0
1
1
B
0
1
0
1
X
0
0
0
1
IITCT

What this logic looks like in electrical circuits


X = A.B
A = 0, B = 0, X=0 Light is off
AND Gate
IITCT

What this logic looks like in electrical circuits


X = A.B
A = 1, B = 1, X=1 Light is on
AND Gate
IITCT

The logic used can also be drawn out on a diagram
IITCT

And Gate
- X = A.B
IITCT

Alarm System



A = Alarm Set
B = Door Sensor Opened
X = Alarm Sounding
A
B
X (A.B)
0
0
0
0
1
1
1
0
1
1
1
1
IITCT

OR Example

X=A+B
Alarm Set
A = Window Opened
B = IR Sensor Detects
movement
X = Alarm Sounding
A
B
X
0
0
0
0
1
1
1
0
1
1
1
1
IITCT

The Boolean logic gates we have discussed are NOT
exhaustive


There are a lot more gates which can be used with
increasing complexity
Example
•
•

XOR
XAND
Later on in the course these logic gates will be used to
carry out mathematical functions
IITCT

Why we learn this



Boolean logic is used in electronics and computers to
carry out actions
Programming Languages use this logic to test conditions
It is the basis of all computing
IITCT

Summary of what we have discussed

Boolean Logic