CSE 111 Information Representation in the Digital World

Analog vs. Digital Faucet Example  Consider a faucet  Digital  Water can be flowing or NOT flowing from the faucet Two States  On  Off  Analog  How much water is flowing from the faucet? How many different answers can there be to this question?

Analog vs. Digital Faucet Example  Advantages of Digital  Replication Analog  Try replicating the exact flow from a faucet Digital  Try replicating ON or OFF

Analog vs. Digital Advantages of Digital Circuits  Replication  Error Correction/Detection Small errors don’t propagate  Miniturization of Circuits  Programmability Digital computers are programmable

The Digital System Two discrete values are used in digital systems. How are discrete elements represented?  Signals are the physical quantities used to represent discrete elements of information in a digital system.  Electric signals used:  Voltage  Current

The Digital System Representation of Binary Values

The Digital System Representation of Binary Values  Why are there voltage ranges instead of exact voltages?  Variations in circuit behavior & noise

The Binary System Why use binary?  Natural Choice  A switch can be ‘on’ or ‘off’  Two states Binary has two symbols, 1 and 0  A transistor is an automated, electrically controlled switch

The Bit The smallest unit that can represent information Binary Digit Two possible values  1, 0  On, Off  True, False  High, Low  Heads, Tails  Black, White

How many bits does it take?  One bit can represent two numbers (0, 1)  2 1 = 2  Two bits can represent four numbers (00, 01, 10, 11)  2 2 = 4  Three bits can represent eight numbers (000, 001, 010, 011, 100, 101, 110, 111)  2 3 = 8  Four bits can represent how many numbers?  2 4 = 16  Ten bits can represent how many numbers?  2 10 =1,024  64 bits can represent how many numbers?  2 64 =18,446,744,073,709,551,616  Note the importance of the math!  You’re NOT going to enumerate all possible combinations and count them to answer this question!

Bits & Bytes Nibble  4 bits  Older term, not widely used today Byte  8 bits Word  The number of bits a microprocessor can process at a single time  Most of today’s processor have a 32-bit word size  64-bit is quickly becoming the norm

Data Representation Bits are grouped to represent both data and instructions in a digital system Coding Techniques  Defines how bits are grouped together to represent information  Types  Numeric  Character  Error Detection/Correction

References Donald D. Givone, Digital Principles and Design, McGraw-Hill, 2003