# Binary

## Ethymology

15th century Latin binarius “dual, twofold, double” from bini "twofold, two apiece, two-by-two".

## Usage

Binary can be both a noun and adjective, it can describe two stars locked in an endless orbit to one another, binary star. In mathematics a base two number, a number that has only two digits zero and one. Finally, when referencing two believed opposites man and woman, on or off.

## The logic

Its hard to imagine someone born in 1815 would lay the foundations for modern day computing. George Boole an English born mathematician on a quest to discover the nature of truth created a symbolic logic using 0s and 1s. 1 representing true and 0 for false (binary logic). Binary logic manipulates 0s and 1s and is ideal for electrical circuits where the use of a switch (transistor) can predetermine the flow of electrical current, it also has further advantages for storing data.

The smallest unit of size in binary is one bit which comes from its contraction of **b**inary dig**it**. One bit represents either zero or one, just like a light switch on (1) or off (0). Now if I string eight bits together I get one byte, with two possible values per bit times eight would look as a base 2 exponent like this 2^{8} which is equal to 2×2×2×2×2×2×2×2. One byte has a range from 0 to 255 (256 possible variations).

Bits in a byte | ||||||||
---|---|---|---|---|---|---|---|---|

Values | 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |

Bit | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

Decimal value | 0 | |||||||

Represents |

* Usage:* For calculations click on the desired bit(s).

Each time you increase the number of bits by one, the number of possible outcomes is also doubled. Just like in the one grain of rice story "Rani is given an amount of rice each day for thirty days: one grain of rice on day one, two grains of rice on day two, four grains of rice on day three " and so on.

In the early 1900’s an Austrian Ludwig Wittgenstein accredited with the creation of the truth table the logic used in integrated circuits today a simplified version shown below.

Truth table | ||||
---|---|---|---|---|

Input | Gate | |||

A | B | Conjunction A AND B |
Disjunction A OR B |
Negation NOT A |

True | True | True | True | False |

True | False | False | True | False |

False | True | False | True | True |

False | False | False | False | True |

With the use of a gate where two inputs A and B can be switched on or off we can perform hardwired operations of logic that result in one output.

### AND Gate

Only when all inputs are true then the output is true.

### OR Gate

When any input is true the output is true.

### NOT Gate

The output is the opposite of the input also known as an inverter, it has only one input.

There are other gates such as XOR, NAND, NOR and XNOR let us not over complicate things. These symbols are used to plan integrated circuits (IC’s) which make the chips present in hardware that makes up our computers.

## The presentation

Code can be written in a multitude of languages all are just sets of instructions that are compiled or translated into machine code, 1s and 0s. The central processor then executes this machine code telling controllers where to turn on or off electrical current. Images, videos data in general is all encoded or decoded from its binary form with sets of instructions, these sets of instructions are standards. Standards help us all to share text, sound or graphic with one another.