Binary Notation The world reduced to 0s 1s

Binary Notation The world reduced to 0’s & 1’s

What are binary numbers? l l l l Decimal system uses ten symbols to represent numeric information 0 1 2 3 4 5 6 7 8 9 Each position within a number represents 10 raised to a power Binary system uses two symbols to represent numeric information 0 1 Each position within a number represents 2 raised to a power Binary numbers can be converted to decimal numbers and vice versa

Using binary numbers l Binary numbers can be used for mathematical operations n 101 + 110 = 1011 l Binary numbers can be used to represent characters n Morse n S. . . U Code. . - S. . . A. - N -.

Binary symbol representation l Two numbers/symbols can be represented in many ways n 0 1 n On Off n True False n Yes No n Open Closed

Binary & Boolean Logic Gottfried Wilhelm Liebniz l (1646 - 1716) l Logic from verbal state to absolute mathematical condition l Influenced by ‘I Ching’ l l George Boole (1815 - 1864) Boolean Algebra n Two Object l n On / Off, True / False Three Operations l AND / OR / NOT

How does Boolean Logic work?

Why do computers use binary? l Must have a way to represent data and instructions l Minimum representation uses two symbols l Binary is the smallest numbering system with only two symbols, 0 & 1 l Binary numbers combined with Boolean logic create circuits capable of mathematical and logic operations

Not every computer used binary The Eniac, Electronic Numerical Integrator and Computer, used a decimal system

Binary symbol representation There are five different ways to represent binary symbols within a computer Some volatile - some more permanent

Integrated Circuits l Electrical l Multiple transistors on silicon chip l Open - electricity can flow - 1 l Closed l Volatile l CPU l Ram representation - no electrical flow - 0

Wire Connections l Electrical l 1. 8 l 0 representation volts (or greater) - 1 volts - 0 l Volatile l System bus

Magnetic l Magnetic properties of iron oxide particles covering a surface l Particles in one direction - 1 l Particles in opposite direction - 0 l Non-volatile l Hard disk

Optical l Reflective l Burned l Not surface with burned areas - Pit -1 burned - Land - 0 l Non-volatile l CD l DVD

Solid State l Trapped electrons in a grid pattern with gates l Open -1 l Closed -0 l Non-volatile l Flash Drive

How binary notation represents data l Bit n - binary digit on / off, 1 / 0, true / false, open / closed l Byte - eight bits n Smallest unit for storing data

How binary notation represents data l Numeric data l Numbers in binary l Instructions l Coded patterns of 0’s & 1’s l Characters l Encoding systems

Encoding Systems ASCII Unicode American Standard for Information Interchange EBCDIC Extended Binary Coded Decimal Interchange Code One Byte Two Bytes One Byte 256 possible characters 65, 000+ possible characters 256 possible characters A = 0100 0001 A = 0000 0100 0001 A = 1100 0010 DOS and Windows to Windows 98 Windows NT, Windows 2000, Windows XP IBM Mainframe

Who is behind encoding l Standards l The Organizations Unicode Consortium l American National Standards Institute - ANSI l Institute of Electrical and Electronics Engineers - IEEE l International Organization for Standardization - ISO

Using binary notation for other data l Analog signal n Continuous l Digital n Set waves signal of numbers n Can be used to describe a wave n Can also be used to recreate a wave