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REPRESENTING INFORMATION:
BINARY, HEX, ASCII
CORRESPONDING READING:UDC CHAPTER 2
CMSC 150: Lecture 2
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
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
0 0000
1 0001
2 0010
3 0011
4 0100
5 0101
6 0110
7 0111
8 1000
9 1001
A 1010
B 1011
C 1100
D 1101
E 1110
F 1111
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
