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Turn in Project 2c

A solution to 2c will be posted after the grace day

Project 2d must be time stamped Friday (2:00AM) for Friday turn-in

Notice there are extra credit components to it

More Digital Representation

Discrete information is represented in binary (PandA), and “continuous” information is made discrete

Return To RGB

Images are constructed from picture elements (pixels); color uses RGB light

The RGB color intensities are specified by 3 numbers in the range [0, 255], ie 1 byte each

Black = [ 0, 0, 0] 0000 0000 0000 0000 0000 0000

Gray = [128,128,128] 1000 0000 1000 0000 1000 0000

White = [255,255,255] 1111 1111 1111 1111 1111 1111

Colors

Colors use different combinations of RGB

Husky Purple

Red=160

Green=76

Blue=230

Positional Notation

The RGB intensities are binary numbers

Binary numbers, like decimal numbers, use place notation

1101 = 1x1000 + 1x100 + 0x10 + 1x1

= 1x10³ + 1x10² + 0x10¹ + 1x10⁰

except that the base is 2 not 10

1101 = 1x8 + 1x4 + 0x2 + 1x1

= 1x2³ + 1x2² + 0x2¹ + 1x2⁰

Binary Numbers

Given a binary number, add up the powers of 2 corresponding to 1s

1010 0000

0x2⁰ = 0x1 = 0

0x2¹ = 0x2 = 0

0x2² = 0x4 = 0

0x2³ = 0x8 = 0

0x2⁴ = 0x16 = 0

1x2⁵ = 1x32 = 32

0x2⁶ = 0x64 = 0

1x2⁷ = 1x128 = 128

= 160

Binary Numbers

Given a binary number, add up the powers of 2 corresponding to 1s

0100 1100

0x2⁰ = 0

0x2¹ = 0

1x2² = 4

1x2³ = 8

0x2⁴ = 0

0x2⁵ = 0

1x2⁶ = 64

0x2⁷ = 0

= 76

Binary Numbers

Given a binary number, add up the powers of 2 corresponding to 1s

1110 0110

0x2⁰ = 0

1x2¹ = 2

1x2² = 4

0x2³ = 0

0x2⁴ = 0

1x2⁵ = 32

1x2⁶ = 64

1x2⁷ = 128

= 230

Husky Purple

Recall that Husky purple is (160,76,230) which in binary is

1010 0000 0100 1100 1110 0110

160 76 230

Suppose you decide it’s not “red” enough

Increase the red by 16 = 1 0000

1010 0000

+ 1 0000

1011 0000

A Redder Purple

Increase by 16 more

00110 000 Carries

1011 0000

+ 1 0000

1100 0000

The rule: When the “place sum” equals the radix or more, subtract radix & carry

Find Binary From Decimal

The conversion algorithm

Start: x is the number to convert

1. Let d the largest numbers so 2^d £ x

2. Is d ³ 0, i.e. more digits to process? No, end

3. Is x ³ 2^d, i.e. is x at least as large as 2^d?

3t. Yes, the binary place is 1; x=x-2^d

3f. No, the binary place is 0

4. d = d - 1, go to Step 2

Find Binary From Decimal

Start: x is the number to convert

1. Let d the largest numbers so 2^d £ x

2. Is d ³ 0, i.e. more digits to process? No, end

3. Is x ³ 2^d, i.e. is x at least large a 2^d?

3t. Y, binary place=1;x=x-2^d

3f. N, binary place=0

4. d = d - 1, go to Step 2

Another Example

Convert x = 141 to binary …

1. Let d the largest numbers so 2^d £ x

2. Is d ³ 0, i.e. more digits to process? No, end

3. Is x ³ 2^d, i.e. is x at least large a 2^d?

3t. Y, binary place=1;x=x-2^d

3f. N, binary place=0

4. d = d - 1, go to Step 2

Digitizing

“Continuous” information like light and sound must be made “discrete”

Information Processing

Manipulating pixels is an example of “computing on a representation”

Photoshop & other graphics SW manipulate pictures by computing on representation

Audio is edited similarly to remove coughs and other odd sounds, speed up, etc.

Searching the dictionary is another example

Bits Are It

Bits represent information, but their interpretation gives bits meaning

0000 0000 1111 0001 0000 1000 0010 0000

Could be a number, color, instruction, ASCII, sound samples, IP address, …

Summary

Bits can represent any information

Discrete information is directly encoded using binary

Continuous information is made discrete

“Computing on representations” is the key to “information processing”

Bias-free Universal Medium Principle


	Turn in Project 2c
			A solution to 2c will be posted after the grace day
	Project 2d must be time stamped Friday (2:00AM) for Friday turn-in
			Notice there are extra credit components to it


	Discrete information is represented in binary (PandA), and “continuous” information is made discrete


	Images are constructed from picture elements (pixels); color uses RGB light
			The RGB color intensities are specified by 3 numbers in the range [0, 255], ie 1 byte each
			Black = [ 0, 0, 0] 0000 0000 0000 0000 0000 0000
			Gray = [128,128,128] 1000 0000 1000 0000 1000 0000
			White = [255,255,255] 1111 1111 1111 1111 1111 1111


	Colors use different combinations of RGB
			Husky Purple
			Red=160
			Green=76
			Blue=230


	The RGB intensities are binary numbers
	Binary numbers, like decimal numbers, use place notation
			1101 = 1x1000 + 1x100 + 0x10 + 1x1
			= 1x10³ + 1x10² + 0x10¹ + 1x10⁰
	except that the base is 2 not 10
			1101 = 1x8 + 1x4 + 0x2 + 1x1
			= 1x2³ + 1x2² + 0x2¹ + 1x2⁰


Given a binary number, add up the powers of 2 corresponding to 1s
	1010 0000
		0x2⁰ = 0x1 = 0
		0x2¹ = 0x2 = 0
		0x2² = 0x4 = 0
		0x2³ = 0x8 = 0
		0x2⁴ = 0x16 = 0
		1x2⁵ = 1x32 = 32
		0x2⁶ = 0x64 = 0
		1x2⁷ = 1x128 = 128
		= 160


Given a binary number, add up the powers of 2 corresponding to 1s
	0100 1100
		0x2⁰ = 0
		0x2¹ = 0
		1x2² = 4
		1x2³ = 8
		0x2⁴ = 0
		0x2⁵ = 0
		1x2⁶ = 64
		0x2⁷ = 0
		= 76


Given a binary number, add up the powers of 2 corresponding to 1s
	1110 0110
		0x2⁰ = 0
		1x2¹ = 2
		1x2² = 4
		0x2³ = 0
		0x2⁴ = 0
		1x2⁵ = 32
		1x2⁶ = 64
		1x2⁷ = 128
		= 230


Recall that Husky purple is (160,76,230) which in binary is
		1010 0000 0100 1100 1110 0110
		160 76 230
	Suppose you decide it’s not “red” enough
		Increase the red by 16 = 1 0000
		1010 0000
		+ 1 0000
		1011 0000


Increase by 16 more

		00110 000 Carries
		1011 0000
		+ 1 0000
		1100 0000

	The rule: When the “place sum” equals the radix or more, subtract radix & carry


	The conversion algorithm
			Start: x is the number to convert
			1. Let d the largest numbers so 2^d £ x
			2. Is d ³ 0, i.e. more digits to process? No, end
			3. Is x ³ 2^d, i.e. is x at least as large as 2^d?
			3t. Yes, the binary place is 1; x=x-2^d
			3f. No, the binary place is 0
			4. d = d - 1, go to Step 2


	Convert x = 141 to binary …
			1. Let d the largest numbers so 2^d £ x
			2. Is d ³ 0, i.e. more digits to process? No, end
			3. Is x ³ 2^d, i.e. is x at least large a 2^d?
			3t. Y, binary place=1;x=x-2^d
			3f. N, binary place=0
			4. d = d - 1, go to Step 2


	“Continuous” information like light and sound must be made “discrete”


	Manipulating pixels is an example of “computing on a representation”
			Photoshop & other graphics SW manipulate pictures by computing on representation
			Audio is edited similarly to remove coughs and other odd sounds, speed up, etc.
			Searching the dictionary is another example


	Bits represent information, but their interpretation gives bits meaning
			0000 0000 1111 0001 0000 1000 0010 0000
			Could be a number, color, instruction, ASCII, sound samples, IP address, …


	Bits can represent any information
		Discrete information is directly encoded using binary
		Continuous information is made discrete
		“Computing on representations” is the key to “information processing”
		Bias-free Universal Medium Principle