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Binary Notation The world reduced to 0’s & 1’s What are binary numbers? 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 Binary numbers can be used for mathematical operations 101 + 110 = 1011 Binary numbers can be used to represent characters Morse S ... U Code ..- S ... A .- N -. Binary symbol representation Two numbers/symbols can be represented in many ways 0 1 On Off True False Yes No Open Closed Binary & Boolean Logic Gottfried Wilhelm Liebniz (1646 - 1716) Logic from verbal state to absolute mathematical condition Influenced by ‘I Ching’ George Boole (1815 - 1864) Boolean Algebra Two Object On / Off, True / False Three Operations AND / OR / NOT How does Boolean Logic work? Why do computers use binary? Must have a way to represent data and instructions Minimum representation uses two symbols Binary is the smallest numbering system with only two symbols, 0 & 1 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 Electrical representation Multiple transistors on silicon chip Open - electricity can flow - 1 Closed Volatile CPU Ram - no electrical flow - 0 Wire Connections Electrical representation 1.8 0 volts (or greater) - 1 volts - 0 Volatile System bus Magnetic Magnetic properties of iron oxide particles covering a surface Particles in one direction - 1 Particles in opposite direction - 0 Non-volatile Hard disk Optical Reflective surface with burned areas Burned Not - Pit -1 burned - Land - 0 Non-volatile CD DVD Solid State Trapped electrons in a grid pattern with gates Open -1 Closed -0 Non-volatile Flash Drive How binary notation represents data Bit - binary digit on / off, 1 / 0, true / false, open / closed Byte - eight bits Smallest unit for storing data How binary notation represents data Numeric data Numbers in binary Instructions Coded patterns of 0’s & 1’s Characters 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 0000 0100 0001 A = 1100 0010 DOS and Windows to Windows 98 Windows NT, Windows 2000, Windows XP IBM Mainframe Who is behind encoding Standards Organizations The Unicode Consortium American National Standards Institute - ANSI Institute of Electrical and Electronics Engineers - IEEE International Organization for Standardization - ISO Using binary notation for other data Analog signal Continuous waves Digital signal Set of numbers Can be used to describe a wave Can also be used to recreate a wave