REPRESENTING INFORMATION:BINARY, HEX, ASCII

CORRESPONDING READING:UDC CHAPTER 2

CMSC 150: Lecture 2

Controlling Information

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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

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 JokeTHERE 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. Hex0 00001 00012 00103 00114 01005 01016 01107 0111

8 10009 1001A 1010B 1011C 1100D 1101E 1110F 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