Notes

Outline

Announcements 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 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