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 2d £ x
			2. Is d ³ 0, i.e. more digits to process? No, end
			3. Is x ³ 2d, i.e. is x at least as large as 2d?
			3t. Yes, the binary place is 1; x=x-2d
			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 2d £ x
			2. Is d ³ 0, i.e. more digits to process? No, end
			3. Is x ³ 2d, i.e. is x at least large a 2d?
			3t. Y, binary place=1;x=x-2d
			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 2d £ x
			2. Is d ³ 0, i.e. more digits to process? No, end
			3. Is x ³ 2d, i.e. is x at least large a 2d?
			3t. Y, binary place=1;x=x-2d
			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 2d £ x
			2. Is d ³ 0, i.e. more digits to process? No, end
			3. Is x ³ 2d, i.e. is x at least large a 2d?
			3t. Y, binary place=1;x=x-2d
			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 2d £ x
			2. Is d ³ 0, i.e. more digits to process? No, end
			3. Is x ³ 2d, i.e. is x at least large a 2d?
			3t. Y, binary place=1;x=x-2d
			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 2d £ x
			2. Is d ³ 0, i.e. more digits to process? No, end
			3. Is x ³ 2d, i.e. is x at least large a 2d?
			3t. Y, binary place=1;x=x-2d
			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 2d £ x
			2. Is d ³ 0, i.e. more digits to process? No, end
			3. Is x ³ 2d, i.e. is x at least large a 2d?
			3t. Y, binary place=1;x=x-2d
			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 2d £ x
			2. Is d ³ 0, i.e. more digits to process? No, end
			3. Is x ³ 2d, i.e. is x at least large a 2d?
			3t. Y, binary place=1;x=x-2d
			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 2d £ x
			2. Is d ³ 0, i.e. more digits to process? No, end
			3. Is x ³ 2d, i.e. is x at least large a 2d?
			3t. Y, binary place=1;x=x-2d
			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 2d £ x
			2. Is d ³ 0, i.e. more digits to process? No, end
			3. Is x ³ 2d, i.e. is x at least large a 2d?
			3t. Y, binary place=1;x=x-2d
			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 2d £ x
			2. Is d ³ 0, i.e. more digits to process? No, end
			3. Is x ³ 2d, i.e. is x at least large a 2d?
			3t. Y, binary place=1;x=x-2d
			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