Binary II

Binary Numbers

Section II

Physical representation

What number system--base 2, binary; base 10, decimal, or the base of any other integer-- is best for machines? The answer depends on how many ways the number system can be represented. There are several ways in nature that one can create binary numbers. For example, a switch is open or closed, and a magnet has a north and a south pole. The principal device currently being used is the transistor, which is either on or off. Some uncommon devices are Josephson junctions and light switches. Moreover, circuits made with such 0-1 devices can be analyzed by Boolean algebra. Machines are designed based on binary numbers. Now the question becomes what can be do with binary numbers?

Decimal-Binary Numbers

A partial equivalence table between decimal and binary numbers is shown below.

Decimal		Binary
0		0
1		1
2		10
3		11
4		100
5		101
6		110
7		111
8		1000
9		1001

Floating point numbers can also easily be converted into binary numbers. As you can see binary numbers are constructed using only two digits. As you might imagine, most of us humans find working with binary numbers a strain.

For future reference we need to define a computer bit, byte, and word. A bit is a single 0 or 1. A byte is a string of 8 bits. The number of bytes in a word varies between 2 and 8, but 8-byte words are becoming increasingly common. Before bytes were designated, a string of six bits defined a character. By shifting from six to eight bits to define a character with the introduction of System 360 in the 60s , IBM was able to define 4 times as many characters in the new character size and at the same time place the competition at a disadvantage.

Using the binary number system we can perform all arithmetic operations

1.) Addition

Decimal		Binary
2		10
+3		+11
====		====
5		101

2.) Multiplication:

Decimal		Binary
Mult	Add	Add
3	3	11
x2	+3	+11
====	====	====
6	6	110

Note: Multiplication can be performed by repeated addition.

Letters

To process letters in a computer each letter or character is assigned a number. Currently the possible numbers in an 8-bit byte are usually used to define characters. There are several competing conventions. To illustrate the process let us use the widely used ASCII convention for 8 bit characters.

Letter		ASCII
A		01000001
B		01000010
C		01000011
D		01000100
E		01000101

With the ASCII conventions a computer will interpret the sequence of characters:

01000010,01000101,01000100

as the word BED. In addition, mathematical symbols can also be represented by strings of bits and logically manipulated by computers for example, to invert matrices algebraically or to construct mathematical proofs using software.

Standards

The ASCII convention is an example of an industrial standard. Standards are essential for advances in computing, communication and automation because without standards interaction among machines or even among software packages for a single machine is impossible. For example, communication of information objects, such as a spreadsheet or CAD design, between software programs and devices requires a standard representation. In comparison with the standards for human interaction, the standards for machine interaction are rigid and exacting.

Firms have mixed motives in setting standards. Firms frequently try to set proprietary standards to get customers locked into using their products. However, if each firm were to adopt its own standard, communication between equipment from different vendors would be difficult. In a growing market, one way that standards are set is that participants tend to follow the dominant firm or coalition of firms. Another way standards are set is by consortia and other organizations.

Today, the move is towards open standards to ease the problems of creating systems of multivendor equipment. Standards expand the market and allow the small firms to seek niches knowing their specialty can be meshed with other equipment.

One example of a search for a standard is the representation of all languages in the world. Obviously, oriental languages which use pictures require larger words than languages which build words out of characters. There is a debate. It appears that 16 bits should suffice. Once a standard is set and accepted worldwide, wordprocessors will be able to process any language easily.

As future managers you should be aware that in markets where there are no standards, equipment can become obsolete overnight if new standards are adopted.

Surf the Net: Check out the following sites promoting various standards.

American National Standards Institute
Unicode Home Page Organization promoting a standard representation for all languages. Unicode is taking over the browser world
Welcome to ISO Online Organization promoting quality standards.

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