Representing information: binary, hex, ascii Corresponding Reading: UDC Chapter 2
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Transcript of Representing information: binary, hex, ascii Corresponding Reading: UDC Chapter 2
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REPRESENTING INFORMATION:BINARY, HEX, ASCII
CORRESPONDING READING:UDC CHAPTER 2
CMSC 150: Lecture 2
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Inside the Computer: Gates
AND Gate
Input Wires
Output Wire
0
1
0
0's & 1's represent low & high voltage, respectively, on the wires
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Inside the Computer: Gates
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Representing Information We need to understand how the 0's and
1's can be used to "control information"
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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)
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Example: your favorite number…8,675,309
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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)
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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
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Example 8,675,30910
=
1000010001011111111011012
Fewer available digits in binary: more space required for representation
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Converting Binary to Decimal For each 1, add the corresponding power
of two
10100101111012
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Converting Binary to Decimal For each 1, add the corresponding power
of two
10100101111012 = 530910
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Now You Get The JokeTHERE ARE 10 TYPES OF PEOPLE IN THE
WORLD:
THOSE WHO CAN COUNT IN BINARY
AND THOSE WHO CAN'T
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Too Much Information?
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Too Much Information?
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Too Much Information?
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An Alternative to Binary? 1000010001011111111011012 = 8,675,30910
1000001001011111111011012 = 8,544,23710
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An Alternative to Binary? 1000010001011111111011012 = 8,675,30910
1000001001011111111011012 = 8,544,23710
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An Alternative to Binary? What if this was km to landing?
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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
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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
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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?
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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
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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?
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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
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Binary vs. Hex0 00001 00012 00103 00114 01005 01016 01107 0111
8 10009 1001A 1010B 1011C 1100D 1101E 1110F 1111
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Converting Binary to Hex Moving right to left, group into bits of
four Convert each four-group to
corresponding hex digit
1000010001011111111011012
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Converting Hex to Binary Simply convert each hex digit to four-bit
binary equivalent
BEEF16 = 1011 1110 1110 11112
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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)
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Our Idea A: 0 B: 1 C: 2 … Z: 25 a: 26 b: 27 … z: 51
, : 52 . : 53 [space] : 54 …
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ASCII: American Standard Code for Information Interchange
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ASCII: American Standard Code for Information Interchange
'A' = 6510 = ???2
'q' = 9010 = ???2
'8' = 5610 = ???2
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ASCII: American Standard Code for Information Interchange
256 total characters…
How many bits needed?
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The Problem with ASCII What about Greek characters? Chinese?
UNICODE: use 16 bits
How many characters can we represent?
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The Problem with ASCII What about Greek characters? Chinese?
UNICODE: use 16 bits
How many characters can we represent?
216 = 65,536
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You Control The Information What is this? 01001101
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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