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Objective: Explain the use of binary numbers to represent a wide variety of phenomenon in computation and communication. Also explain why binary numbers are preferred in creating computation and communication equipment. The index for this section is:
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 |
If your browser displays the table in an unrecognized form, click on the button to obtain the table correctly displayed in a gif picture.
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 |
|
If your browser displays the table in an unrecognized form, click on the button to obtain the table correctly displayed in a gif picture.
2.) Multiplication:
| Decimal | Binary | ||||
|---|---|---|---|---|---|
| Mult | Add | Add | |||
| 3 | 3 | 11 | |||
| x2 | +3 | +11 | |||
====| ==== | ==== |
6 | 6 | 110 |
|
If your browser displays the table in an unrecognized form, click on the button to obtain the table correctly displayed in a gif picture.
Note: Multiplication can be performed by repeated addition.
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 |
If your browser displays the table in an unrecognized form, click on the button to obtain the table correctly displayed in a gif picture.
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.
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 at 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 adopts its own standard communication between equipment from different vendors is 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.
To return to the notes remember to click `back' at the top of your screen. You may have to click several times depending how deeply you delve into these files.
Sound is a single waveform which can be decomposed into pure frequencies. For example, the music of a rock band is a single waveform. Physiologically, however, the listener hears the different instruments and the voice. In its natural state sound in an analog phenomenon-that is a wave phenomenon. By measuring the single waveform at frequent intervals and representing each measurement as a binary number analog sound can be digitized.
The quality of digital sound depends on the frequency at which the sound is measured as well as the size of the word used to represent the wave form. To convert the voice into a telephone quality binary signal the voice is sampled 8000 times a second. The measured waveform is converted into a seven bit binary number with an eighth bit added for error checking. This means a telephone conversation is converted into a stream of 64,000 bits per second. The telephone system is presently analog between telephones and the switchboard, but an increasing portion of long distance phone traffic is being sent digitally. The phone conversation is converted at the telephone exchange (switch) prior to long distance transmission. In the future all telephone conversations will be converted to digital at the phone.( 10 to 30 years) Corporate internal communications are rapidly becoming digital so that the corporation can use the installed telephone lines for simultaneously voice and data transmission. In order to obtain stereo quality sound you need a larger word size (16 bits) and much more frequent sampling to capture the high frequency sounds. One scheme for digital recordings measures the sound 44,000 times a second using a 16 bit( 2 byte) word for 1.4 million bits a second. The new stereo sound TV samples about 36000 times a second and used a 14 to 16 bit word for the measurements.
Surf the Internet: For a very nice page created by MCI demonstrating the affect of the frequency of measurement on the quality of sound, click here. This demonstration requires a multimedia computer for full effect. When finished, click on `back' at the top of your Netscape screen.
Computer graphics: The fundamental characteristic which determines the clarity of a computer screen is number of picture elements which are called pixels. On a computer screen these pixels are arranged in a rectangular grid and the size of the grid varies considerably among computers. For example, if each character is represented by a rectangle of 9 lines and 9 columns then a 80 character by 24 line text display would have a total of 216 lines and 720 columns. For graphic pictures from satellites, 256, 512 and 1024 lines and columns are grid sizes frequently used. On computer screens and television sets there are 4 columns for every 3 lines. In contrast, the aspect ration of movie screens is 16 to 9 (broader field of vision). Currently 640 columns and 480 lines is a fairly common size grid for 14 inch computer screens. For computer assisted design more detail is desirable, hence workstation screens are 16 inch or larger with 1280 columns by 846 lines or greater. For this purpose the new IBM PC2 offer cards with grids up to 1024 by 1024. The number of bits associated with each pixel determines the number of colors that can be represented. For example, black and white, 4, 16, and 256 colors would be represented by pixel of 1,2,4, and 8 bits respectively. Computer graphics are digital, however as humans prefer an analog signal it is sometimes converted to analog just before display.
To avoid flicker on a computer screen the image must be redrawn about 60 times a second. The number of bits of information which must be processed each second to output to a computer screen is the refresh rate times the number of columns times the numbers of rows times the number of bits used to represent each pixel. For current PC's this number can as large as 60 x 640 x 480 x 4 = 73,728,000 bits per second.
The trend in computer screens is higher and higher resolution and greater number of colors. Since for most purposes no more than ten thousand colors are required for quality pictures, this limit may become common. Currently television type monitors are cheaper and better than flat screen displays, such as those in notebook computers. In the future quality flat screen displays may displace television type monitors. Currently, there are many types of competing flat screen technologies.
Surf the Internet:
Remember that the resolution a computer screen is much less than the resolution in a media magazine. A picture in a media magazine generally has 2600 pixels/inch: whereas a picture on a computer screen only has 70 pixels/inch. It is a real challenge to make computer pictures look real. The following list shows examples of different aspects of art, graphics and pictures on the Net. Surf to each example.
There are thousands of sites devoted to art, graphics and pictures. The following provide Yahoo lists of each category:
To communicate over analog phone lines, computer digital information must be converted to an analog signal. This requires a modem. To understand digital to analog conversion and modems, click here for Rockwell Corporation's Baudman. To return to the notes remember to click `back' at the top of your screen. You may have to click several times depending how deeply you delve into these files.
(1) Commercial TV: TV has a single light waveform (analog). The single waveform corresponds to the position of the electron beam as it moves across the TV screen in a 525 (US standard) line zigzag pattern. On one pass the electron beam draws the odd lines and on the next the even lines(interlacing). The entire picture is refreshed, that is redrawn, 30 times a second. Color is represented by adding red, blue, and green light. Current TV is a low resolution device with about 300 columns and 200 lines. Note that when text is presented on a TV screen you almost never see more than 20 characters in a line. If they tried to present 80 characters, all you would see is a blur. TV looks realistic because it is an analog device which displays millions of colors.
To digitize a TV picture the signal is sampled at twice the frequency humans can discriminate, which is about 5 million cycles per second, and the colors represented by a 24 bit word. The resulting raw digital signal varies from 90 million bits to 220 million depending on the standard. The digital signal is converted back to analog for viewing, a process which functions to smooth out the discrete digital points.
Currently there is a commercial battle between Japan, Europe and the US for the next generation of high definition television, HDTV. Japan and Europe both adopted analog standards with approximately double the resolution of current TV. The US to leapfrog the competition has organized a competition between major firms. The final standard is likely to be digital. HDTV will come on line in the next twenty years. To switch to digital TV there must be an inexpensive box which will convert the digital signal to analog for the existing TVs. Also the broadcasting industry will have to see new profit potential to justify the replacement of all their current analog technology. Also, the consumer must be offered new interesting services to want to purchase the new TVs.
To represent voice and pictures, we could have used a number system to base 3, 4, 5, or even 10, our common everyday decimal number system. Why bother with binary numbers which, as is clearly obvious, are difficult to work with. The reason is quite simple. 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. For ease of human use these binary numbers are converted to decimal, text, symbols, voice or image so that humans can easily utilize the information.
What does this mean? The point is that transmission and manipulation of data, words, voice, of pictures occurs through the use of binary numbers. A general purpose communications network with multimedia computers as nodes can manipulate and communicate numbers, words, voice, and images. You don't need special purpose hardware for each phenomenon. Also with the move to digital communication, the communication engineer needs to know is the number of bits he has to transmit per second, but not what is being transmitted.
Fundamental Economic Point: It is much cheaper to have a single computing and communication technology which will compute and communicate data, words, symbols, voice and all types of images than require separate technologies for each.In the marketplace, the boundary line between communications and computer companies is becoming fuzzy. Future competition in the combined computer-communications industry will be fierce. One of the reasons for the breakup of the phone system is AT&T's desire to penetrate the computer market. To counter AT&T's move, IBM has entered the communications market. Neither has had much success in the others territory.
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