AP Computer Science Principles DAT-1 Faculty Lecture on Data Representation

Summary

Professor Paul Tiemman from Rochester Institute of Technology explains how data is internally represented in computers, focusing on binary and decimal number systems. He covers converting binary to decimal and vice versa, emphasizing positional numbering systems and powers of two. The presentation also explores the RGB color model and delves into steganography, demonstrating how to hide messages within digital images by manipulating pixel bits. Tiemman shows that even with significant bit reduction, images can still convey their original content, highlighting the power of digital manipulation and the importance of skepticism when interpreting digital media.

Takeaways

• 😀 Professor Paul Tiemman from Rochester Institute of Technology introduces the concept of data representation in computers, focusing on binary and decimal systems.
• 🔑 The positional numbering system is explained, emphasizing that each digit in a binary number represents a power of 2, which is key to converting binary to decimal.
• 📊 A methodical approach to converting binary to decimal is demonstrated using a chart to identify and sum the relevant powers of 2.
• 🔍 An important check is highlighted for binary to decimal conversion: if the binary number ends in 0, the decimal result must be even, ensuring conversion accuracy.
• 🔄 The reverse process of converting decimal to binary is explained, using a similar chart method but starting with powers of 2 greater than the decimal number.
• 💡 The significance of the least significant bit (LSB) in determining the parity (odd or even) of a decimal number when converting from binary is discussed.
• 🖼️ The concept of image representation in computers using pixels and the RGB color model is introduced, showing how colors are created by combining red, green, and blue intensities.
• 🎨 The potential for steganography in digital images is explored, demonstrating how messages can be hidden by manipulating pixel data without noticeably altering the image.
• 📚 A practical example of steganography is given, where the entire text of 'Alice in Wonderland' is encoded within the least significant bits of a digital image's pixels.
• 🤓 The presentation concludes with a binary joke, emphasizing the importance of understanding binary for computer scientists and highlighting the manipulability of digital data.

Q & A

What is the main topic of Paul Tiemman's presentation?

The main topic of Paul Tiemman's presentation is how data, including numbers, images, and text, is represented internally in a computer using binary numbers.

How does positional numbering system work in the context of binary numbers?

In a positional numbering system, each position in a number represents a particular power of the base of the number. In binary, each bit represents a different power of 2, starting from 2^0 on the right and increasing as you move left.

What is the process for converting a binary number to a decimal number?

To convert a binary number to a decimal, you determine which powers of 2 are represented by the 1s in the binary number and sum those powers. For example, the binary number 1 1 0 0 1 0 1 0 1 0 is converted to decimal by summing 512 + 256 + 32 + 8 + 2, which equals 810.

How can you check if a binary number represents an even or odd decimal number?

If a binary number represents an odd decimal number, the least significant bit (rightmost bit) must be 1. If it's 0, the number is even. This is because all powers of 2, except 2^0, are even.

What is the method for converting a decimal number to a binary number?

To convert a decimal number to binary, you determine which powers of 2 can be subtracted from the number until you reach zero, marking a 1 for each power of 2 used. For example, to convert 453 to binary, you would start with the highest power of 2 less than 453 (which is 256), mark a 1, subtract 256 from 453, and continue this process for the remaining number.

How many unique values can be represented with an 8-bit number?

With an 8-bit number, you can represent 256 unique values, calculated by raising 2 to the power of the number of bits (2^8).

What is the RGB color model and how is it used in computing?

The RGB color model is an additive color model where red (R), green (G), and blue (B) intensities are combined to create various colors. In computing, images are represented by pixels, each with an RGB value, allowing for a wide range of colors to be displayed.

What is steganography and how can it be applied to digital images?

Steganography is the practice of hiding a message within another message or object. In the context of digital images, it involves modifying some of the bits in an image's pixels to encode a hidden message without significantly altering the image's appearance.

How does the presenter demonstrate the encoding of a message in a digital image?

The presenter demonstrates encoding a message by using the least significant bit of the red channel in each pixel to store bits of an ASCII character. The entire text of 'Alice in Wonderland' is encoded in the pixels of an image, with only about half of the pixels being changed, making the alteration nearly imperceptible.

What is the significance of the joke 'There are 10 types of people in the world' mentioned in the presentation?

The joke 'There are 10 types of people in the world: those who understand binary, and those who don't' is a play on the fact that binary is a base-2 number system, which only has two digits, 0 and 1. It humorously implies that there are only two kinds of people: those who can think in binary and those who cannot.

Outlines

00:00

💡 Introduction to Data Representation

Professor Paul Tiemman introduces the topic of data representation in computers, specifically focusing on the conversion between binary and decimal systems. He emphasizes the importance of understanding positional numbering systems, where each position in a number represents a power of the base. In binary, each bit represents a power of 2, and conversion to decimal involves summing the relevant powers of 2. A chart is used to illustrate this process, showing how to determine which powers of 2 to add together based on the binary digits. The professor also discusses a simple check for binary to decimal conversion, noting that the least significant bit must be 1 for odd numbers and 0 for even numbers.

05:03

🔢 Decimal to Binary Conversion

The script continues with the process of converting decimal numbers to binary. A table is used to determine which powers of 2 are needed to sum up to the decimal number. The professor explains that powers of 2 greater than the decimal number are not included. The conversion process involves subtracting each power of 2 that can be included in the sum from the decimal number, moving right to left across the table. The example given is converting the decimal number 453 to binary, resulting in 111000101. The professor also discusses the range of numbers that can be represented with a given number of bits, explaining that 2 to the power of the number of bits gives the total number of unique values that can be represented.

10:04

🖼️ Digital Image Representation

The third paragraph delves into how images are represented in a computer, using the RGB color model where colors are created by combining red, green, and blue intensities. The professor explains that images are divided into pixels, each with a unique color determined by RGB values. The example of Grumpy Cat is used to illustrate how images are broken down into pixels. The concept of steganography is introduced as a way to hide messages within images or other objects. The paragraph concludes with a discussion on the potential for hiding messages within digital images by manipulating bits, suggesting that not all bits are necessary for image representation and some can be used to encode hidden messages.

15:06

🔄 Exploring Bit Manipulation in Images

This section explores the impact of bit manipulation on image quality. The professor demonstrates how turning off the least significant bits in the color channels of an image can reduce the number of colors represented without significantly altering the image's appearance. By turning off bits in the image of a samurai, the professor shows that even with fewer colors, the image remains recognizable. This experiment leads to a discussion about the feasibility of steganography in images, where messages can be hidden by modifying certain bits without noticeably changing the image.

20:08

📜 Encoding a Message in an Image

The professor describes a method for encoding a message into an image using ASCII values. By using the least significant bit of the red channel in each pixel, an 8-bit ASCII character can be stored across eight pixels. The example given is encoding the text 'Alice in Wonderland' into an image of Hobbiton. The professor explains that only about half of the pixels need to be changed to embed the message, making it difficult to detect the alteration. The paragraph concludes with a reminder that images on a computer can be easily manipulated and may not always represent reality, and ends with a binary-related joke to emphasize the importance of understanding binary in computer science.

Keywords

💡Binary Number

A binary number is a base-2 numeral system that uses only two symbols, 0 and 1, to represent numerical values. In the context of the video, binary numbers are the fundamental way data is represented inside a computer. The script explains how to convert binary numbers to decimal and vice versa, which is essential for understanding how computers process and store data. For example, the script demonstrates converting the binary number '1 1 0 0 1 0 1 0 1 0' to the decimal number 810.

💡Decimal Number

A decimal number is a base-10 numeral system that uses the ten digits from 0 to 9 to represent values. The video script discusses converting decimal numbers to binary, which is a common operation in computer science. This is important for understanding how numerical data is encoded in a format that computers can process. The script provides a method to convert the decimal number 453 into its binary equivalent.

💡Positional Numbering System

A positional numbering system is a system where each position in a number represents a different power of the base. The video emphasizes that binary is a positional system where each digit (bit) represents a power of 2. This concept is crucial for understanding how to convert between binary and decimal systems, as each bit's value is determined by its position and whether it is a 0 or 1.

💡Bit

A bit is the basic unit of information in computing and digital communications, representing a logical state with one of two possible values, 0 or 1. The script uses the term 'bit' to describe the individual elements of a binary number, and it is through the manipulation of bits that data representation and processing in computers occur.

💡RGB Model

The RGB model is an additive color model in which red, green, and blue light are added together in various ways to reproduce a broad array of colors. The video script explains that images in a computer are represented using the RGB model, where each pixel's color is determined by the intensity of red, green, and blue components. This model is essential for understanding digital image representation and manipulation.

💡Pixel

A pixel, short for 'picture element,' is the smallest addressable element in a display device; it is the basic unit of a digital image. The script describes how an image is divided into pixels, each with a specific color value, to form the complete picture. This concept is key to understanding how images are stored and processed within a computer.

💡Steganography

Steganography is the practice of concealing a message, image, or file within another message, image, or file. The video script introduces steganography in the context of hiding messages within digital images by manipulating pixel data. This technique is used to demonstrate the potential for data manipulation and the importance of being aware of what digital media may contain beyond its surface appearance.

💡ASCII

ASCII (American Standard Code for Information Interchange) is a character encoding standard for electronic communication, which represents text in computers and telecommunications equipment. The script mentions ASCII in the context of encoding text messages within images using the least significant bits of pixel color values. This illustrates how text can be hidden within images using steganography.

💡Project Gutenberg

Project Gutenberg is mentioned in the script as a source for classic books in text form, which can be used for embedding text within images as part of a steganography demonstration. The script uses Project Gutenberg to obtain the text of 'Alice in Wonderland,' highlighting the vast amount of textual data that can be hidden within a single image.

💡Manipulation of Digital Media

The script discusses the ease with which digital images can be manipulated to hide information or alter their appearance. This concept is important for understanding the potential for deception in digital media and the importance of critical evaluation of digital content. The video uses the example of embedding a text message within an image to demonstrate the manipulation of digital media.

Highlights

Introduction to data representation in computers, focusing on binary and decimal systems.

Explanation of positional numbering systems and their application in binary.

Conversion of binary numbers to decimal by summing powers of two.

Use of a chart to visualize the conversion process from binary to decimal.

Crossing out powers of two where binary bits are zero for easier conversion.

Self-check method for binary to decimal conversion using the least significant bit.

Conversion of decimal numbers to binary by finding the necessary powers of two.

Creating a table to determine which bits are needed for the decimal to binary conversion.

Determining the range of numbers representable by a given number of bits.

Understanding that 0 is a value and its importance in binary counting.

The concept of steganography and its application in hiding messages.

Hiding a message within a digital image by manipulating pixel bits.

The impact of reducing color depth on image quality and visibility of changes.

Encoding a message using ASCII and the least significant bit of pixel color channels.

The potential to store large texts within images using steganography.

Embedding the entire text of 'Alice in Wonderland' into a digital image.

The importance of critical thinking when interpreting digital images.

Final thoughts on the versatility of binary data manipulation and a parting joke.

Transcripts

hi my name is paul tiemann and i'm a

professor at the rochester institute

technology in rochester new york

and what i want to do today is talk to

you about how

data is represented internally in a

computer

some of this will probably be a review

which i think is probably a good thing

and

hopefully some of it will be new and

you'll learn something interesting along

the way

so the first thing i thought i would do

is just kind of start with some simple

stuff that i'm sure you've seen before

but i want to make sure we're all on the

same page before we get

too far into this and what i want to

just do is go over

converting binary numbers to decimal and

decimal numbers to binary so let's

take looking at a binary number to

decimal first

okay as you probably learned in class

we use numbering systems that are

referred to as positional numbering

systems

and the reason we call them positional

numbering systems is because each

position in the number represents

a particular power of the base of the

number that we're representing here so

in binary each one of the binary digits

or bits

represents a different power of 2. so

what we need to do if we want to convert

a binary number

from binary to decimal what we basically

need to do is figure out what powers of

2 we need to add together

and adding those powers together will

tell us what the number is

now the way i typically do this is i'll

draw myself a little chart

and i'll put the binary number in the

chart so you'll see here in the top row

i've got the number that i want to

convert and in the bottom it's blank at

the moment

and now what i'll do is i'll just simply

fill in

the powers of two that each one of those

bits represents

okay so starting over at the right hand

side we start with one

you're always going to start with one

regardless of the base you're working in

because any number raised to zero is

going to be

one and then since i'm working in binary

as i work my way from right to left what

i just simply do is multiply by two

so you see it's one two four eight

sixteen so on up to five hundred and

twelve

okay so that's the start now the nice

thing about converting

a binary number to decimal is when we

look

at the binary digits there's only two

possibilities there's either gonna be a

one or a zero

and the nice thing is if the bit is a

zero it means that the power is not in

the sum

so what i will also do in my little

chart typically is i will just simply

cross out

any of the values where the bits are

zero okay

and in this particular case that leaves

the powers of 2 512

256 32 8 and 2 and what i do is i add

those together

and i get 810 so i know that the

binary number 1 1 0 0 1

0 1 0 1 0 is equivalent to the decimal

number 810

now another thing that i always like to

do is kind of have a way of checking

myself to make sure that i did things

right

and there's a simple little check that

you can do in

these binary conversions just to kind of

make sure that things are

you know at least you got something

close to the right answer

and what that has to do with is

basically that power of two to the zero

okay uh if you take a look at all the

powers of two with the exception of two

to the zero which is one they're all

even

which means if i am representing an odd

number in binary that

bottom bit or the least significant bit

has to be set to a one

so i can look at that binary number one

one zero zero one zero one zero

one zero without even converting it

because it ends in zero i know it's an

even number

and so what i always do is kind of a

self check is i make it double check

and i say to myself since my binary

number ends in zero

the decimal value that i get as a result

of the conversion must be even as well

okay if it's not if i get an odd decimal

value then i know i did something wrong

i'm going to go back and check my work

okay so that's converting binary to

decimal and i find that really simple to

do

okay now let's take the flip side you're

given a number in decimal and you have

to convert that to binary

all right again i'm going to start it

out basically the same way i'm going to

do my little table

and i want to figure out what powers are

going to be

powers of two i need to add together

here to get 453

so what i've done you'll see in this

case is i filled the powers in the

bottom row

and i've left the top row blank because

i need to figure out

whether the corresponding bit for each

one of those columns is either a zero or

a one

the other thing that i want you to kind

of notice and hopefully

you spotted it right off the top of your

head 453

is an odd number so i know whatever

answer i get here that least significant

bit where

we have two to the zero it has to be a

one and if it's not i did something

wrong when i did the conversion

now another question that you might want

to ask yourself is

how do i know how many powers of 2

how many columns i'm going to put in

this table all right

remember what i'm trying to do here is i

want to figure out the powers of 2 that

i need to add together

to get the number 453

if i have a power of 2 that's greater

than 453 like 512

512 can't possibly be one of the numbers

that i need to add together to get 453

so what i'll do when i'm generating my

table is i'll happily double my numbers

until i hit the first power of two

that's greater than the number that i'm

trying to convert

so that's why i stopped at 512 here

okay and the next thing i'll do is i'll

pop a zero in that column just to remind

myself

that power is not going to be in this

number all right

so now the question is how do i do the

conversion well the way i use the table

and the way that i do the conversion

here

is i'll work my way in this particular

case from left to right

and for each power i'll ask the question

can i subtract that power from the

number i'm trying to convert

so i have 256 256 is less than 453

so i know that the power 256 has to be

in the binary number

that's going to be the equivalent 453

so what i'm going to do is i'm going to

put a 1 above 256 as a reminder that

that's going to be

in the resulting binary number and then

the other thing i'm going to do is i'm

going to take 453 i'm going to subtract

256 from it

because i've accounted for that number

already that leaves me with 197.

and so now as i work my way down the

table and i consider the next column

i'm going to be looking at 197 and not

453

okay and as i work my way across i look

at 128 128 is less than 197

so i'll put a 1 up there and as i did

before i'll compute what the difference

is

working my way down the line i see that

64 is less than 69

so again i'll put a one up there okay

and now i only have five left

the next column is the column that

represents 32

well that can't be in it it's too big

16 can't be in it because it's too big

eight can't be in it because it's too

big

that gets me down to four well four is

going to be in there

so i'll take uh put a one above the four

as you're reminded that that's it that

bit is turned on in this particular

binary representation

i'll subtract four from five i have a

one left

um two is bigger than one so there'll be

a zero there

and lo and behold i have one left so i'm

gonna put a one above

and i've accounted for all the numbers

and so

reading the binary number off the table

i can see that 453 decimal

is equivalent to 1 1 1 0

0 0 1 0 1 in binary

and again what i want you to notice is

we spotted upfront ahead of time

that 453 is an odd number so is

one one one zero zero zero one zero one

because it ends in a one okay so there's

a little bit of confidence that we got

it right

now the other thing that i want to uh

again

just go over real quick and again i

think this is a review but this is going

to be very pertinent to what i'm going

to show you in a minute

is i want to ask the question if i

have a certain number of bits that i'm

going to use to represent a number

what's the range of numbers that i can

represent in that number of bits

okay and what i did here just so that we

have a kind of a

concrete point is how many unique values

can i represent in an

8-bit number but you should be able to

answer this question really for

binary numbers that have an orbit you

know any number of bits

okay so how can we figure this out well

a lot of times what i like to do

is i like to kind of try to walk very

slowly to get to the solution so

what i'll ask myself first here is well

what if i only have one bit how many

unique values can i represent

using one bit well with one bit

i can either represent zero or i can

represent one

and what that means is i have two values

okay what if i jump up to two bits now

well if i jump up to two bits

you can see i now have four values

all right and if you take a look at that

table you'll

kind of notice a pattern if you look in

the left the right hand

column you're going to notice it goes 0

1

0 1 which is exactly the one bit

pattern but it's duplicated twice and

then if you look at the column on the

left hand side you're going to see that

i put a zero

in front of the first repetition from

that

two bit from that one bit table and then

one in front of and that's how you get

four

right what about three bits

okay well here's three bits and again

with three bits you can see that it's

going to be eight unique values and

again

the same pattern applies so doing this

it sort of looks like

we could say well it looks like if you

take

two raise it to the number of bits that

you have

that's going to give you the number of

values at least that applies to these

three cases here

so let's try that out okay let's try it

for four bits

according to that postulation we made on

the previous slide

this should be we should be able to

represent 16 values using four bits

all right well with four bits the

largest number that i can represent

in binary is one one one one and if you

do a quick conversion in your head

you'll realize that that's

15 decimal okay so what that means is in

four bits

i can count one two three

up to 15 using four bits but you might

look at that and say but

that's only 15 values and it seems to

break the rule that you came up with

on the previous slide but we left out

something really important

and this is something that comes up over

and over and over again in computing

you've got to remember that 0 is also a

value that we can represent

so when we look at counting i actually

start counting at

0. and if i start counting at zero and

if i go up to 15

while the maximum value that i can

represent is

15 there are actually 16 unique values

there

so it does work so in general what we

can say

is you take the number of bits you raise

two to that

so using eight bits to answer the

question we had on that very first slide

uh using eight bits i can represent a

total of 256 different values

for n bits i can represent two to the n

different values

okay so like i said that should just be

a review i think it's something that

you've probably seen before

um you may have done it a little bit

differently but sometimes looking at

something in

different perspectives gives you a

little bit more insight into it

okay the big thing i want you to

remember from this

presentation is that if something is in

the computer

it's nothing but this and i don't care

what it is i don't care if it's numbers

that we just looked at

images videos this presentation you're

looking at is inside a computer

it's nothing but bits all right just the

crazy stream

of zeros and ones that's everything

that's inside that universe of the

computer

now at first you might think that

there's rather limiting

but it's actually kind of empowering

because

if we have things that are represented

in bits and they're in the computer

something that a computer is really good

at is manipulating bits

so once it's in digital form once it's

in the computer

once it's represented as a stream of

zeros and ones

it can be very easily manipulated by a

program

and that's basically what i want to talk

about next

so before i get into that again a quick

review

i i'm going to do some image stuff here

and i want to remind you

how images work inside a computer the

first thing we need to do is delve a

little bit because

color science and there's a variety of

different models that color scientists

use to

to understand and represent and model

colors

one that is commonly used in computing

is a model that's called rgb where r

stands for red g

stands for green and b stands for blue

and it's an

additive color model where you create

colors

by adding together different intensities

of those three

basic colors and that little diagram

that i have on the right there

that it's it basically looks like a venn

diagram

is showing you very simply if i don't

vary

the the intensity of the rgb components

you can see that using those three

different colors it's actually

possible to represent a total of seven

different colors you can see

the red the green and the blue and then

you can see the yellow

uh the purple and whatever color that is

with the

odd g and the b plus white in the middle

okay

and i guess theoretically you could say

there's an eighth color in there

which is good for computers because we

love powers of two

the black is also a color that's

represented there as well

okay so how do we represent images

inside a computer

well this is a picture of my very first

cat his name is grumpy cat

and grumpy cat was called grumpy cactus

he was a little bit strange he would

always want to get petted

but as soon as you petted him he would

bite you and it wasn't like a

love bite it was like i'm drawing blood

so that's why we called him grumpy so

this is

obviously a picture of grumpy he's

obviously in the computer

at him but the images and the question

is well

how do we represent this as a stream of

bits

well commonly a very common way of

representing an image is we'll take an

image and we'll divide it up into a

number of different cells

all right so what i've done here is i've

laid a grid over the picture of grumpy

all right basically this is being done

at a much

finer scale in this image in fact the

scale of these squares is so small

that your eyes can't discern them all

right and that's

kind of the magic here each one of those

individual cells is referred to as a

pixel

and each pixel has one unique color

associated with it

and that color is based on

an r a g and a b value all right

now it's a little bit hard to see the

granularity here so what i did is i took

just grumpy's eye and i blew it up

at 800 percent and now you can actually

start to see the pixels

that make up his eye okay and if you

look carefully

you'll see that each one of those pixels

has

its own color associated with it all

right and that's

basically how images are represented

inside a computer

and again i expect it's a bit of a

review

one thing that i want to just note is

that

there are many different schemes that

you can use to do the rgb

or the rgb model namely one of the

things that you can differ is the number

of bits

what i'm going to do here is assume that

we're using eight bits for each of those

color channels

um so we have eight bits for red eight

bits for green and eight bits for blue

and using eight bits for those three

colors we can represent more than

16 million different colors okay

all right now what i wanted to

do is talk about um

a technique called steganography and

steganography it sounds really

complicated

but it's something that's been around

forever and it's the practice of hiding

a message within another message or

within another physical object

okay and if you take a look at that

second sentence there

laura's spending echoed assorted

priorities for accurate skateboard use

you might kind of look at that and say

that's a little bit of a weird sentence

but i guess then it makes sense

but what i've actually done is i've

embedded a message inside of that

and until i tell you how to decode that

message you don't know what it is

but i will tell you if you look at the

second

letter in each of the words in that

sentence

it will give you a hidden message so if

i

what i did here is i just bolded them

and maybe you can see it now

and it's still a little bit noisy but if

i just pull those out

you'll see that the message is apcs

rocks

that's steganography it's been around

forever

and there's lots of classic examples of

it um if this is something of interest

you i strongly encourage you at some

point

google steganography sometime and find

out about it

so why am i bringing this up well what

i'm wondering is

can we hide a message inside of a

digital picture

the answer is going to be yes and so the

question is

how can i go about doing that all right

well

if i want to hide a message inside a

digital picture

what i'm going to have to do is modify

some of the bits in that

picture to encode the message all right

kind of like what i did in the previous

sentence it was a pain to come up with

i had to come up with words that had the

right second letter in it

all right and i need to kind of do the

same thing here i need

to change some of the bits in the

picture

now i've already mentioned that in an

8-bit

rgb image we can in one pixel i can

represent 16 million different colors

so a question might be is

do we really need all 24 of those bits

at what point is a kind of overkill

either our eyes can't tell the

difference you know can our eyes

finally determine the difference between

more than 16 million different colors i

know mine certainly cannot

and another question is well what about

the resolution of the device

that i'm displaying the image on a

typical computer or a cell phone

the resolution is probably not going to

be that good anyway

so even though we have 16 million

different

color possibilities the display itself

may not

actually be able to show them so the

question that i kind of want to ask

is if i take a picture and if i start

mucking around with some of the bits in

the picture

at what point do i notice it so this is

a picture of me

uh when i was in new zealand and i

thought i'd stop

at um this happens to be a samurai at

the same wise genji's house

from the hobbit i'm checking to see if

anybody's home

all right and this is the original

picture that i took with my cell phone

uh the basic model that you're seeing

here is exactly what i described

all right there's uh 24 bits here that

are being used for each pixel

and what i did here is i wrote a program

that took this picture and went through

all the pixel values and turned off

the least significant bit so what i did

here and that's what i'm trying to say

at the top

is the x the first seven bits in every

one of those color channels i left them

alone

but i turned the last one off so now

instead of using 24

bits to represent the color i've cut it

down to 21 bits

and using 21 bits i can still represent

a little bit more than 2 million colors

and i'm going to flip back and forth

here for a minute

but it's pretty hard to tell that i did

anything to that picture

well what about turning off another bit

all right so here i've turned off the

last two bits

and so now i'm down to 18 bits i have

a possibility of 262 different colors

now

all right but again i think as i go back

and forth

you're going to see at least i don't i

don't

notice much of the difference here i've

turned off

the last three bits so now i'm down to

32 000 colors

all right and let's go one step further

let's go to four

and now i've turned off the bottom four

bits

so now you have 496 different colors

that i use

and i think you can finally at least i

can see it for sure

you can start to see some differences in

the picture

and the easiest place to spot them is

look at the shadows on the hobbit door

if you look you the the shadow almost

seems pixelated at this point

and it makes sense if you think about it

because i have

fewer shades of that door color to work

with

and so it's going to be harder to for

the image to make a smooth

transition from the dark color

to the light color from the shadow to

the light

okay and i think i went one step further

to kind of push it out one

little bit more here i've turned off all

the bottom five bits and now you can see

is the

the effect is really noticeable at this

point all right

i find it absolutely kind of remarkable

that even after turning off five bits

in each one of the colored channels in

each one of the pixels in this picture

you can still see the image it's it it's

really kind of remarkable and it shows

you

how much extra information is actually

encoded in those pictures

okay so let's get back to steganography

now so what can i do

well what i want to do is we're computer

people

so what i want to do is i want to encode

my message but i'm going to do it using

ascii

so here's an ascii table standard ascii

table you've probably seen something

like this before

i remember that ascii is just the

character mapping and what it does is it

maps

characters to numbers so if i want to

represent for example a capital a

in the computer i do that with a decimal

number 65

or if i were going to look at in binary

it would be 0 1

0 0 0 0

so what i'm going to do is the way that

i'm going to encode my message

is i'm going to take just the least

significant bit

of the red channel of every single

pixel to store one bit of an eight bit

ascii character

so what i'm going to do is i'm going to

take that 8-bit representation of the

ascii character

and i'm going to store it in eight

different pixels

the most significantly in the first

pixel the next bit will be after that

and so on down the line

okay um the hobbiton picture

is rough it's not roughly it is 13 1383

pixels high by 1945

wide that means there's more than two

and a half million pixels in that image

which means if i'm going to use eight of

these for each ascii character

i can store 350 000

characters in that message using this

scheme that's just using the red channel

i could also use the blue and the greek

channel if i wanted to

so what am i going to stick in there we

you can literally stick any text in

there that you want but what i thought i

would do is pick

something that you might recognize and

something that has some heft to it and

what i did is i searched around

online and there's a website called

project gutenberg

and project gutenberg's been around for

a long long time and what

they actually do is they they were the

first people that i'm aware of that had

ebooks in a way

what they've done is they've taken many

classic

books and they've converted them to text

form

so if you ever want to get the text from

a you know a book

it's got to be a classic book usually

you'll find it on project gutenberg

so i went to project gutenberg and i got

the entire text of the story alex and

alice in wonderland turns out there's

166

657 characters in that text

it'll easily fit in my picture so how am

i going to encode it this is just a

picture of what i was trying to describe

before

i'm showing you the first eight um

our red values in my hobbiton picture

and in the first eight what i want to do

is store the a

which we saw was zero one zero zero

zero zero zero zero one all right and

you can see what i've done

i'm going to put that most significant

bit at the first rgb

then the second bit and the next one and

so on down the line and what i've done

here is i've just shown you

the a and the l and if you look at the

right hand column

that's the modified value that i'm going

to write out for

that r value and you're going to see

that not all of these get

changed and that makes sense because

it's going to be the case that only

about 50 of the time

i'm going to need to actually change one

of these bits which means it's going to

be even

harder for you to observe a change in

the image

from embedding this message inside of it

and so

you know long story short this picture

that you see here

looks a lot like the very first picture

that i showed you

um but you'll just have to take my word

for it

that what i've done here is this met

this particular picture

actually has the entire story alice in

wonderland

encoded in the pixels in the picture in

the case you're curious

um i needed about um

when i take a look at the changes out of

all the changes that i made i only

changed about

half of the pixels in the picture and

again

that just points out the fact it's a

little bit harder to

for your eyes to see so really the

takeaway that i want you to see here

is that a once we have things in a

binary form in the computer we can do

some pretty cool things with it

and b and this is really an important

thing that

i'm sure you will discuss at some point

in your csp class

when you see an image on a computer it

may not necessarily be real

it is very easy to manipulate pictures

make them look like something totally

different from what they actually are

okay and then the last thing i thought i

would leave you with

is a joke well sort of a joke but

this is a nerdy kind of a joke there are

one zero types of people in this world

those who understand binary

and those who don't so now that you're

becoming a computer scientist

you can now appreciate what the shirt

means

okay so with that i hope you've enjoyed

this

presentation i had fun putting it

together

and i hope you learned something good

from it have a great day thanks bye