Base 2 Numbering SystemChapter 1

Binary and Character Encoding

• Modern humans use character sets (or alphabets) to represent written sounds and words. Each symbol or letter has its own phonetic sound. The letter (or combination of letters, such as “ph”) is paired to its corresponding sound, forming a character code. It is through the combination of symbols or letters that words are generated and phrases, and ultimately complex communication.

Computer to Computer Communication

• Computers, however, have yet to evolve to a level capable of exactly duplicating the complex processing-consistently-and-reliably-of the human brain. Currently, computers can best communicate with other computers in a manner based upon the principles of fundamental Mathematics. Computer to human communication, while having evolved to a certain degree of voice replication, and other advances, it is still based upon the principles of fundamentals mathematics.

Binary Number System

The current methodology for digital data transfer is called binary, and it is the basis for all computing technology.To understand how computers handle, move, store, access, save, delete or otherwise manipulate data, you must understand the binary system.

What is Binary?

• Binary is the name given to a Base 2 numbering system or encoding scheme. As the name Base 2 implies, there are two and only two possible states (1 or 0). This encoding scheme works well with electronic communication. There are only two states (on or off, yes or no, 1 or 0, open or close). If you’re talking about circuits open and closed works well

Communication in a Two State Universe

• Communication in a two-state environment is now possible. (yes or no, on or off, 1 or 0). This is important being that presently computer essentially pass or store information as either electrical or magnetic states.

Electricity and Magnetism

• Magnetism – is the force whereby objects are attracted to or repelled by one another. Usually these objects are metal such as iron.

• Magnetism can1. Store electricity (aka battery)2. Generate electricity (aka generator)

Magnetism has Two States• Two states or opposing poles

1. Positive2. Negative

• Magnetic states can also be contained or preserved.

Similarities between magnetic fields and electric fields:

• Electric fields are produced by two kinds of charges, positive and negative. Magnetic fields are associated with two magnetic poles, north and south, although they are also produced by charges (but moving charges).

• Like poles repel; unlike poles attract • Electric field points in the direction of the force experienced by a positive

charge. Magnetic field points in the direction of the force experienced by a north pole.

• Differences between magnetic fields and electric fields: – Positive and negative charges can exist separately. North and South

poles always come together. – Electric field lines have definite starting and ending points. Magnetic

field lines are continuous loops. Outside a magnet the field is directed from the north pole to the south pole. Inside a magnet the field runs from south to north.

Magnetic Domain

Magnetic Domain – is a series of atoms that point their poles in the same direction. Example: Direction of an iron oxide shaving can be manipulated by a magnet.

Bar Magnet• Is made up of a group of domains. • The most common source of magnetic fields

is the electric current loop.• Electricity is the type of activity arising from

the existence of charge. The basic unit of charge is that on the:– Proton – positive– Electron - negative

Electricity• Electricity tends to move or flow in its active

state.– Electricity is a good representing data in motion.– Magnetism is good at representing data at rest.

• Both have two separate and opposing states, and allows for Base 2 digital communication.

• The movement of digital data is easily represented by the two states of electricity or magnetism and is conveniently presented by 1 or 0 respectively.

Building Blocks: The Origins of Data

• Bit – A single zero (0) or a single one (1). Smallest unit of data recognized or processed by a computer.

• Binary is the basic building blocks of a communication system for silicon-based technologies. (Computers, Mobile phone, etc..)

Bit

• With a single bit, we are limited to only two choices 1(yes or on) or 0 (no or off). By adding another bit (two bits), you double the possible outcomes. (00,01, 10, 11)

Growing the Building Blocks of Data

• As you connect consecutive 0’s and 1’s (Bits) together, the ability to represents an increasingly larger set of characters, and words increases geometrically.

• Example:– 1 Bit 0 or 1– 2 Bits 00, 01, 10, 11– 3 Bits 000, 001, 010, 011, 100, 101, 110, 111

Power of Zero

What is 2 to the power of 0?First let’s study the law of exponentsn^x/n^y = n^(x – y)

Example:2^4/2^2 = 2^(4-2) = 2^2 = 4

Power of Zero First we need to establish that a number divided by itself is 1. Examples: 3/3 = 1, 5/5 = 1, 125/125 = 1Then we can say the following:

1 = 2^4/2^4 = 2^(4-4) = 2^0

Why is this important? It allows us to understand the geometric growth of possible states or outcomes attained by combining bits.

Power of 2

American Standard Code For Information Interchange

• History of ASCII: (Wikipedia definition)

Abbreviated from American Standard Code for Information Interchange, is a character-encoding scheme. Originally based on the English alphabet, it encodes 27 = 128 specified characters into 7-bit binary integers as shown by the ASCII chart on the right. The characters encoded are numbers 0 to 9, lowercase letters a to z, uppercase letters A to Z, basic punctuation symbols, control codes that originated with Teletype machines, and a space. For example, lowercase j would become binary 1101010 and decimal 106.ASCII codes represent text in computers, communications equipment, and other devices that use text. Most modern character-encoding schemes are based on ASCII, though they support many additional characters.

BYTE

• English-language personal computers used in America employ a seven bit character code called ASCII, which allows for a character set of 128 items of upper- and lower – case Latin letters, Arabic numerals, signs, and control characters. ASCII also serve as a foundation of the Universal Character Set (UCS).

• The eighth bit is used as a parity bit, with its value used for checking whether or not data have been transmitted properly.

• Eight bits equal one byte which gives us a character code of 256.

ASCII

Character Codes: The Basis for Processing Textual Data

• Textual data is also numerical data to a computer.• The circuitry of the microprocessor that lies at the heart of a

modern computer system can only do two things:1. Calculate Binary Arithmetic operations2. Perform Boolean (true or false) logic operations

• A character code pairs a character set, such as an alphabet, with a decimal and/or binary system.

Character Code• The max characters possible in a character

code depends upon numbering system and number of bits.

• More bits in the character code, the bigger the character set.

• Computer operates more efficiently when processing data in bytes. Most common is 8, 16, 32, 64 bits. Using a 10 bit or 15 bit or other non multiple of 8 character code is inefficient to handle in a computer.

Extended ACII and Unicode

• Extended ASCII is an eight-bit encoding scheme that includes the standard seven-bit ASCII characters as well as other.

• Unicode – is a character coding system designed to support the world wide interchange, processing, and display of the written texts of the diverse languages.

• Unicode – 16 bit coding scheme will allow for 65,536 potential outcomes which allow us to cover most of