Computer Logic

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Computer Logic Logic Gates

• Justin Champion

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IITCT

• Contents
• Introduction to Logic
• Look at the different Logic Gates
• Summary

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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.
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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

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IITCT

• You can only get into the night club if you have
  a coloured suit

True Get into Club
False Refused Entry to Club
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IITCT

• Logic
• As seen you use this all the time
• If (suit coloured) then
• Entry to club
• Else
• 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

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IITCT

• You can only get into the club if you have a
  coloured suit and a hat on your head!

False Refused
True Accepted
False Refused
False Refused
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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

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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

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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

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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

Flow
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IITCT

• Processors use large numbers of these transistors
  to make decisions
• AMD 3200 processor has 54.3 Million transistors!

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IITCT

• Example Truth Tables

A B A.B AB A AB
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)
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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
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IITCT

• Try a truth table yourself
• Create a truth table for
• If man has long hair and not a member entry
  refused

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IITCT

• Answer
• Create a truth table for
• If person has long hair and not a member entry
  refused

Long Hair Member Not Member Long Hair.Member
0 1 0 Accepted
0 0 1 Accepted
1 1 0 Accepted
1 0 1 Refused
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IITCT

• What this logic looks like in electrical circuits
• First the truth table

A B X
0 0 0
0 1 0
1 0 0
1 1 1
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IITCT

• What this logic looks like in electrical circuits
• X A.B
• A 0, B 0, X0 Light is off

AND Gate
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IITCT

• What this logic looks like in electrical circuits
• X A.B
• A 1, B 1, X1 Light is on

AND Gate
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IITCT

• The logic used can also be drawn out on a diagram

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IITCT

• And Gate - X A.B

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IITCT
A B X (A.B)
0 0 0
0 1 1
1 0 1
1 1 1

• Alarm System
• A Alarm Set
• B Door Sensor Opened
• X Alarm Sounding

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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
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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

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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

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IITCT

• Summary of what we have discussed
• Boolean Logic