Bits, Binary, Boolean Logic and Computers

1
Bits, Binary, Boolean Logic and Computers

• ISAT 252Analytical Methods IV
• Programming and Problem Solving

2
How does a computer work?

• From the moment you flip the switch and
  electricity flows through the power cord and into
  the machine, what is happening? What makes the
  "magic" happen?

3
Objectives

• Goal
• Bridge the gap between 0 and 1 and a cell phone,
  or other modern computers and the applications
  built on them, by
• Understanding key concepts underpinning the
  construction of modern computers
• Boolean logic and truth tables
• Transistors
• Logic gates
• Binary
• Physical manifestation of logic gates in circuit
  boards ? computers

4
Computers are electronic

• Electrons flow through conductors
• Controlling flow ? useful functionality
• Transistors are devices that control flow
• A semiconductor chip has millions of transistors
• As of 2006, the threshold of one billion
  transistors on a single computer chip has been
  broken

5
What is a transistor?

• Arguably the single most important invention of
  the 20th century
• The core component underlying the computer and
  most other modern electronic devices
• A transistor is an electronic device that is
  capable of implementing the basic operations
  involved in Boolean algebra

6
What is Boolean algebra?

• The simplest Boolean algebra has
• Two elements 0 and 1
• Two binary operators AND, OR
• One unary operator NOT
• And is defined by the basic rules

7
Why is Boolean algebra cool?

• Boolean algebra represents a complete set of
  logical operations
• The inputs and outputs of Boolean algebraic
  expressions can always be reduced to a minimal
  set of two elements, namely 0 and 1
• Representing 0 and 1 in a machine is relatively
  straightforward
• Therefore, a machine that can implement Boolean
  operations can theoretically reach any logical
  conclusion

8
How does it work?

• In practice, ones and zeroes are mapped to
  represent more abstract ideas like "true" or
  "false," "red" or "blue," "chicken" or "fish"
• Example
• 0100 0000 A
• capital letter 'A' in ASCII (American Standard
  Code for Information Interchange)
• but we're getting ahead of ourselves

9
So, how do transistors work?

• Great intro to semiconductors
• http//computer.howstuffworks.com/diode.htm
• Transistors have 3 terminals
• Source
• Gate
• Drain
• The voltage applied to the gate controls current
  flow from source to drain, i.e. the gate opens
  or closes to let current through

source
gate
drain
10
Building logic gates with transistors

• There are two basic types of transistors
• P-type conduct when voltage 0
• N-type conduct when voltage ? 0
• Multiple transistors are combined to implement
  Boolean logical operations

11
Types of Logic Gates
AND
OR
XOR
NAND
NOR
XNOR
12
What do you do with the gates?

• Gates can be wired together to do useful things
• But you need to understand binary

13
Computers use binary. Why?

• Why do humans count by tens?
• Because we have 10 fingers and therefore it is
  convenient
• Why do computers count by twos?
• Because computers only have 2 "fingers"
• On/off
• Open/closed
• High/low
• 0/1
• Therefore it is convenient for computers to use
  binary to do calculations

14
Getting to Know Binary

• If you don't know binary, here are some places to
  start
• http//en.wikipedia.org/wiki/Binary_numeral_system
  
• http//www.mathsisfun.com/binary-digits.html
• You should, at a minimum, be able to
• Count in binary
• Add 2 binary numbers together
• Subtract 2 binary numbers
• Understand the relationship between binary and
  hexadecimal notation (i.e. be able to convert
  from one to the other)

15
Bits and Binary

• Computers represent information by the existence
  or absence of electrical current, i.e.
• On or Off
• True or False
• 0 or 1
• Binary is a numbering system that makes it
  convenient to do such calculations
• A Binary digIT, or bit, is the smallest unit of
  information that can be stored or manipulated by
  a computer

16
Bridging the Gap

• So, do you understand now how a computer works?
• Could answer questions like
• Why aren't computers creative or intuitive?
• Why did it take until 1996 for a computer like
  Deep Blue to beat Garry Kasparov in chess?
• Do you see how a massive collection of simple,
  but intricately connected, circuits could let you
  to do fun stuff like WoW or IM?
• Will you know better how to troubleshoot your
  machine next time something goes wrong?

17
In Summary

• Don't be intimidated by computers
• It's not impossible to understand how they are
  put together
• Having even a basic grasp of the core components
  inside a computer and how they are put together
  will greatly deepen your ability to manipulate
  computers to help you solve problems
• This is just the beginning!