REPRESENTING INFORMATION: BINARY, HEX, ASCII C ORRESPONDING R EADING : UDC C HAPTER 2 CMSC 150: Lecture 2

Controlling Information Watch Newman on YouTube

Inside the Computer: Gates AND Gate Input Wires Output Wire 's & 1's represent low & high voltage, respectively, on the wires

Inside the Computer: Gates

Representing Information  We need to understand how the 0's and 1's can be used to "control information"

The Decimal Number System  Deci- (ten)  Base is ten  first (rightmost) place: ones (i.e., 10 0 )  second place: tens (i.e., 10 1 )  third place: hundreds (i.e., 10 2 )  …  Digits available: 0, 1, 2, …, 9 (ten total)

Example: your favorite number… 8,675,309

The Binary Number System  Bi- (two)  bicycle, bicentennial, biphenyl  Base two  first (rightmost) place: ones (i.e., 2 0 )  second place: twos (i.e., 2 1 )  third place: fours (i.e., 2 2 )  …  Digits available: 0, 1 (two total)

Representing Decimal in Binary  Moving right to left, include a "slot" for every power of two <= your decimal number  Moving left to right:  Put 1 in the slot if that power of two can be subtracted from your total remaining  Put 0 in the slot if not  Continue until all slots are filled filling to the right with 0's as necessary

Example  8,675, =  Fewer available digits in binary: more space required for representation

Converting Binary to Decimal  For each 1, add the corresponding power of two 

Converting Binary to Decimal  For each 1, add the corresponding power of two  =

Now You Get The Joke THERE ARE 10 TYPES OF PEOPLE IN THE WORLD: THOSE WHO CAN COUNT IN BINARY AND THOSE WHO CAN'T

Too Much Information?

An Alternative to Binary?  = 8,675,  = 8,544,237 10

An Alternative to Binary?  = 8,675,  = 8,544,237 10

An Alternative to Binary?  What if this was km to landing?

The Hexadecimal Number System  Hex- (six) Deci- (ten)  Base sixteen  first (rightmost) place: ones (i.e., 16 0 )  second place: sixteens (i.e., 16 1 )  third place: two-hundred-fifty-sixes (i.e., 16 2 )  …  Digits available: sixteen total 0, 1, 2, …, 9, A, B, C, D, E, F

Using Hex  Can convert decimal to hex and vice-versa  process is similar, but using base 16 and 0-9, A-F  Most commonly used as a shorthand for binary  Avoid this

More About Binary  How many different things can you represent using binary:  with only one slot (i.e., one bit)?  with two slots (i.e., two bits)?  with three bits?  with n bits?

More About Binary  How many different things can you represent using binary:  with only one slot (i.e., one bit)? 2  with two slots (i.e., two bits)? 2 2 = 4  with three bits? 2 3 = 8  with n bits? 2 n

Binary vs. Hex  One slot in hex can be one of 16 values 0, 1, 2, …, 9, A, B, C, D, E, F  How many bits do you need to represent one hex digit?

Binary vs. Hex  One slot in hex can be one of 16 values 0, 1, 2, …, 9, A, B, C, D, E, F  How many bits do you need to represent one hex digit?  4 bits can represent 2 4 = 16 different values

Binary vs. Hex A1010 B1011 C1100 D1101 E1110 F1111

Converting Binary to Hex  Moving right to left, group into bits of four  Convert each four-group to corresponding hex digit 

Converting Hex to Binary  Simply convert each hex digit to four-bit binary equivalent  BEEF 16 =

Representing Different Information  So far, everything has been a number  What about characters? Punctuation?  Idea:  put all the characters, punctuation in order  assign a unique number to each  done! (we know how to represent numbers)

Our Idea  A: 0  B: 1  C: 2  …  Z: 25  a: 26  b: 27  …  z: 51 , : 52 . : 53  [space] : 54  …

ASCII: American Standard Code for Information Interchange

'A' = = ??? 2 'q' = = ??? 2 '8' = = ??? 2

ASCII: American Standard Code for Information Interchange 256 total characters… How many bits needed?

The Problem with ASCII  What about Greek characters? Chinese?  UNICODE: use 16 bits  How many characters can we represent?

The Problem with ASCII  What about Greek characters? Chinese?  UNICODE: use 16 bits  How many characters can we represent?  2 16 = 65,536

You Control The Information  What is this?

You Control The Information  What is this?  Depends on how you interpret it:  =  = 'M'  = one million one thousand one hundred and one  You must be clear on representation and interpretation