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Representing information: binary, hex, ascii Corresponding Reading: UDC Chapter 2PowerPoint Presentation

Representing information: binary, hex, ascii Corresponding Reading: UDC Chapter 2

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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

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

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

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)

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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