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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

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### Binary Notation

### Binary symbol representation

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 Code -
- S ... U ..- 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

(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

Binary & Boolean LogicWhy 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

There are five different ways to represent binary symbols within a computer

Some volatile - some more permanent

Integrated Circuits Volatile CPU Ram

- Electrical representation
- Multiple transistors on silicon chip
- Open - electricity can flow - 1
- Closed - no electrical flow - 0

Wire Connections Volatile System bus

- Electrical representation
- 1.8 volts (or greater) - 1
- 0 volts - 0

Magnetic Non-volatile Hard disk

- Magnetic properties of iron oxide particles covering a surface
- Particles in one direction - 1
- Particles in opposite direction - 0

Optical Non-volatile CD DVD

- Reflective surface with burned areas
- Burned - Pit -1
- Not burned - Land - 0

Solid State Non-volatile Flash Drive

- Trapped electrons in a grid pattern with gates
- Open - 1
- Closed - 0

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

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

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