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

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.

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

### 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)

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?

• 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

• 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?

• 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

• Idea:

• put all the characters, punctuation in order

• assign a unique number to each

• done! (we know how to represent numbers)

• 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

'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