MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

1.4NumberSystems

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Goal

To appreciate the importance ofbinary and hexadecimal number systems

in the computer world.

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

RowntreeTheater

computer

Let’s take a little trip

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

RowntreeTheater

computer

H BuildingSwitch

Let’s take a little trip

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

RowntreeTheater

computer

H BuildingSwitch

C BuildingSwitch

Let’s take a little trip

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

RowntreeTheater

computer

H BuildingSwitch

C BuildingSwitch

C BuildingRouter

Let’s take a little trip

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

RowntreeTheater

computer

H BuildingSwitch

C BuildingSwitch

C BuildingRouter

Barrie(Bell)

Let’s take a little trip

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

RowntreeTheater

computer

H BuildingSwitch

C BuildingSwitch

C BuildingRouter

Barrie(Bell)

Toronto(Bell)

Let’s take a little trip

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

RowntreeTheater

computer

H BuildingSwitch

C BuildingSwitch

C BuildingRouter

Barrie(Bell)

Toronto(Bell)

Chicago

Let’s take a little trip

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

RowntreeTheater

computer

H BuildingSwitch

C BuildingSwitch

C BuildingRouter

Barrie(Bell)

Toronto(Bell)

Chicago

Los Angeles

Let’s take a little trip

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

RowntreeTheater

computer

H BuildingSwitch

C BuildingSwitch

C BuildingRouter

Barrie(Bell)

Toronto(Bell)

Chicago

Los Angeles

Manila

that’s through undersea cables in the Pacific Ocean

Let’s take a little trip

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

RowntreeTheater

computer

H BuildingSwitch

C BuildingSwitch

C BuildingRouter

Barrie(Bell)

Toronto(Bell)

Chicago

Los Angeles

Manila

Ateneomain router

Let’s take a little trip

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

RowntreeTheater

computer

H BuildingSwitch

C BuildingSwitch

C BuildingRouter

Barrie(Bell)

Toronto(Bell)

Chicago

Los Angeles

Manila

Ateneomain router

Ateneoserver room

switch

Let’s take a little trip

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

RowntreeTheater

computer

H BuildingSwitch

C BuildingSwitch

C BuildingRouter

Barrie(Bell)

Toronto(Bell)

Chicago

Los Angeles

Manila

Ateneomain router

Ateneoserver room

switch Ateneowwwserver

Let’s take a little trip

All the “conversations” done ina matter of seconds.

With data travelling at thespeed of light.

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Let’s take a little tripRowntreeTheater

computer

H BuildingSwitch

C BuildingSwitch

C BuildingRouter

Barrie(Bell)

Toronto(Bell)

Chicago

Los Angeles

Manila

Ateneomain router

Ateneoserver room

switch Ateneowwwserver

Request

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Let’s take a little tripRowntreeTheater

computer

H BuildingSwitch

C BuildingSwitch

C BuildingRouter

Barrie(Bell)

Toronto(Bell)

Chicago

Los Angeles

Manila

Ateneomain router

Ateneoserver room

switch Ateneowwwserver

“Conversations” are encodedas digital signals (binary) for travelacross wires and through the air.

Response

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Let’s take a little tripRowntreeTheater

computer

H BuildingSwitch

C BuildingSwitch

C BuildingRouter

Barrie(Bell)

Toronto(Bell)

Chicago

Los Angeles

Manila

Ateneomain router

Ateneoserver room

switch Ateneowwwserver

And what’s amazing is thatdata reaches us intact and

with no errors (most of the time).11101011

10110100

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Pictures are stored as bits

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Songs are stored as bits

MATH1003

10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001

Binary, Decimal, Hexadecimal

Binary is the language of the computer.Decimal is the human number system.Hexadecimal is used to bridge the two.