1. COMT 222 Tools for a Digital World

2. 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

3. 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

4. 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

5. Binary Numbers Converting to and from binary  Position values: 9876543210 5122561286432168421

6. Binary/Decimal Conversion Convert to decimal:  1  11  111  1111  1010 Convert to binary: 27

7. 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

8. 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?) 0123456789ABCDEF 0123456789101112131415

9. Bit Groups as Hex Digits 00000 10001 20010 30011 40100 50101 60110 70111 81000 91001 A1010 B1011 C1100 D1101 E1110 F1111

10. Hex to and From Decimal 3210 4096256161 Convert  180 to hex  0x3e to decimal

11. 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