COMT 222

Tools for a Digital World

Digital?

• What makes information Digital?

• If it helps: When is information not analog?

• Answer: A finite number of “symbols” A fixed time associated with a symbol

OK, so what is a symbol?

• Conveys a digital value

• Transmitted at a given “symbol rate”, i.e. A circuit sends a certain number of symbols per

second A symbol takes a fixed amount of time to send

• In practice a symbol represents a certain number of bits

Binary

• Is the simplest form of a digital symbol

• Each binary “symbol” can represent either a 0 or a 1

• If a unit of information (often called a symbol) is one bit long, it can send two values

Binary Numbers

• Converting to and from binary Position values:

9 8 7 6 5 4 3 2 1 0

512 256 128 64 32 16 8 4 2 1

Binary/Decimal Conversion

• Convert to decimal: 1 11 111 1111 1010

• Convert to binary: 27

A related issue

• Given a number of bits, how many symbols can you make? 1 bit: 0 to 1 2 bits: 00 to 11 3 bits: 000 to 111

Hexadecimal

• Binary numbers have lots of digits• Using another number system allows

grouping of bits• Hexadecimal digits (and their values):

(What is 15 in binary?)

0 1 2 3 4 5 6 7 8 9 A B C D E F0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Bit Groups as Hex Digits

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

Hex to and From Decimal

3 2 1 0

4096 256 16 1

• Convert 180 to hex 0x3e to decimal

Application - ASCII

• Text is digital

• Need to agree on “encoding”

• What string of bits do we assign to COMT 222

• ASCII (in hex) 43 4F 4D 54 20 32 32 32