Transcript Representing information: binary, hex, ascii Corresponding Reading

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
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
(rightmost) place: ones (i.e., 100)
 second place:
tens (i.e., 101)
 third place:
hundreds (i.e., 102)
…
 first

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)

Base sixteen
Deci- (ten)
(rightmost) place: ones (i.e., 160)
 second place:
sixteens (i.e., 161)
 third place:
two-hundred-fifty-sixes (i.e., 162)
…
 first

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)?
with two slots (i.e., two bits)?
with three bits?
with n bits?
2
22 = 4
23 = 8
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
8
1000
1
0001
9
1001
2
0010
A
1010
3
0011
B
1011
4
0100
C
1100
5
0101
D
1101
6
0110
E
1110
7
0111
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