Binary

Main Page :: Binary

Binary is a form of counting that uses a base-2 system, a counting system with 2 digits. Binary uses only '0' and '1', which relates to an electrical 'low' (0) or 'high' (1) signal. This can conceptually be extended to 'false' (0) or 'true' (1).

In computing, binary is used for all forms of calculations. Larger values are expressed as being 'X-bits', where 'X' is the number of 'BInary digiTs' used to create the value. Modern computers generally use multiples of '8' bits, as 8 bits are referred to as a byte, or the smallest really usable unit.

A string of bits are given a relative value, where each subsequent bit is given twice the value as the bit beside it. Which side of the string of bits we start counting from is called 'Endianess', and is either 'Big Endian', where the least significant bit (smallest value bit) is on the left side of the string, or 'Little Endian', where the least significant bit in on the right side. For the rest of this article, we will be using 'Little Endian' in out examples.

For the sake of humans, a table called 'Hexadecimal' was created to more easily represent a collection of four bits as a value between [0-9,a-f]. These four bits are themselves referred to as a nibble. This is a rarely used term however, because for practical purposes, the sixteen values represented is just too small to represent enough data.

To allow for a more usable set of values, 8-bit strings where used to represent 255 possible strings, and these combinations of 8 bits were referred to as 1 byte; The smallest effective unit of storage used by modern computers.

In the early days of computing, a common standard called ASCII was created using the lower 128 possible combinations of these 255 possibly combinations of zeros and ones. This ranged from 0 (binary: 0000 0000) to 127 (binary: 0111 1111). The upper 128 possible combinations where left for vendor-specific definitions.

In this way, operating systems that supported the ASCII standard could understand one another's basic data. These lower 128 possible combinations of binary data would always represent the same things on all the different systems!

For example, the character capital 'A' is represented as the binary value '0100 0001' (Hex: '41'), which is the 101st combination on the ASCII table. Alternatively, lower-case 'a' is represented as the binary value '0110 0001' (Hex: '61'), which is in turn the 141st possible combination on the ASCII table.

As a side note, this is why to a computer, capital 'A' and lower-case 'a' are not the same thing. A computer sees two different binary values!

 

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