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Representing information: binary, hex, ascii Corresponding Reading: UDC Chapter 2. CMSC 150: Lecture 2 . Controlling Information. Watch Newman on YouTube. Inside the Computer: Gates. AND Gate. 0. 0. Input Wires. 1. Output Wire.

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Representing information:binary, hex, asciiCorresponding Reading:UDC Chapter 2

CMSC 150: Lecture 2


Controlling Information

Watch Newman on YouTube


Inside the Computer: Gates

AND Gate

0

0

Input Wires

1

Output Wire

0'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., 100)

    • second place: tens (i.e., 101)

    • third place: hundreds (i.e., 102)

  • 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., 20)

    • second place: twos (i.e., 21)

    • third place: fours (i.e., 22)

  • 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

  • 8,675,30910

    =

    1000010001011111111011012

  • Fewer available digits in binary:

    more space required for representation


Converting Binary to Decimal

  • For each 1, add the corresponding power of two

  • 10100101111012


Converting Binary to Decimal

  • For each 1, add the corresponding power of two

  • 10100101111012 = 530910


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?


Too Much Information?


Too Much Information?


An Alternative to Binary?

  • 1000010001011111111011012 = 8,675,30910

  • 1000001001011111111011012 = 8,544,23710


An Alternative to Binary?

  • 1000010001011111111011012 = 8,675,30910

  • 1000001001011111111011012 = 8,544,23710


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., 160)

    • second place: sixteens (i.e., 161)

    • third place: two-hundred-fifty-sixes (i.e., 162)

  • 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)? 22 = 4

  • with three bits? 23 = 8

  • with n bits? 2n


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 24 = 16 different values


Binary vs. Hex


Converting Binary to Hex

  • Moving right to left, group into bits of four

  • Convert each four-group to corresponding hex digit

  • 1000010001011111111011012


Converting Hex to Binary

  • Simply convert each hex digit to four-bit binary equivalent

  • BEEF16 = 1011 1110 1110 11112


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


ASCII: American Standard Code for Information Interchange

'A' = 6510 = ???2

'q' = 9010 = ???2

'8' = 5610 = ???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?

  • 216 = 65,536


You Control The Information

  • What is this? 01001101


You Control The Information

  • What is this? 01001101

  • Depends on how you interpret it:

  • 010011012 = 7710

  • 010011012 = 'M'

  • 0100110110 = one million one thousand one hundred and one

  • You must be clear on representation and interpretation


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