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PC911 > How-To > Miscellaneous > Understanding the Binary System

Bits vs. Bytes

Ok, now that we understand the binary system and how binary numbers work, let's take a closer look at how your computer uses this system. Earlier we talked about 1 and 0 being binary digits. That's an ugly phrase to use, so let's abbreviate it by combining the two words into a nice short term: Bit. Sound familiar? Thought so.

In our earlier example, we used the binary number 10101110. This number has 8 binary digits, or 8 bits. This is not a coincidence, because if you take a group of 8 bits, you have a byte. The reason we have to group bits is that if you are being fed a continuous stream of bits you have no idea where one piece of information ends and the next one starts. But if you receive groups of defined length, e.g. a byte containing 8 bits, it's easy to interpret them. A good example is how ASCII code (American Standard Code for Information Interchange) works. Any character you type on your keyboard is interpreted by your computer as a byte, an 8 digit binary number. For example, the letter "A" is expressed as the ASCII code 65. But 65 is a decimal number, so if you convert it to a binary number, you get 01000001. These 8 digits, or one byte, are known to your computer as the letter "A".

It is very important to know the difference between a bit and a byte because these two can get easily confused. One good example is monitoring data transfer speed. When you download a file from the Internet, you probably have noticed that your browser indicates the transfer rate in KBps. Please note that the letter "B" is capitalized. This means the transfer rate is shown in Kilo Bytes per second. For example, your download might arrive at a rate of 3.5 KBps. Now, if you are using a 56K modem, why is that rate so low, shouldn't you see something closer to 56? No, because 56K is short for 56 Kbps. Note the lower case "b", it means Kilo Bits per second. And since we know that 8 bits equal one byte, we divide 56 by 8 and get a theoretical maximum of 7 Kilo Bytes per second.





A GigaByte does not necessarily equal a GigaByte

Here's another situation where you can look really smart if you paid attention and know the difference between the binary and the decimal system. This question is asked over and over again:

"I bought a 8.4GB hard drive, but when I formatted it, Windows tells me that I have only 7.82 GB available. Did they sell me the wrong drive?"

No, they sold you the correct drive, but it was not labeled quite correctly. The marketing department of the drive manufacturer doesn't know too much about bits and bytes and the binary system. To make it easier to calculate, they assume that 1 KB is 1000 Bytes, 1 MB is 1000 KB, etc. which is wrong. So when they have a drive that can hold 8,400,000,000 Bytes, they just call it 8.4 GB and say that's close enough for government work. Not so.The multiplication factor is not 1000 since we're not using the decimal system, it is 1024 instead (2 to the power of 10).

To figure out the correct size of that drive, divide 8,400,000,000 Bytes by 1024 and you'll get 8,203,125 KB. Divide that by 1024, and you get 8,010 MB. Divide that by 1024 and you get 7.82 GB which is the actual size of your hard drive in GB as reported by your operating system.

Of Pits and Grooves

A CD stores data using the binary system in the following matter: When writing data to a CD, the laser does nothing else than following a spiral-shaped "guide groove" while burning the data as a long string of pits into a reflective dye layer on the CD. When the CD is read later, a laser follows the same spiral and reads either a pit where the light does not get reflected very well, or a smooth area called land where the light reflects very well. This system is nothing else but our good old binary system, using only two possible states, pit or land, to read and record data in binary format, 0 or 1.

Magnetic storage

Storing data on a magnetic media, such as a hard drive, also uses the binary system. In a very simplified manner of speaking, each data bit gets stored on a drive as a tiny magnetic field. Each magnetic field has two poles, North and South. When the disk spins around and data is read by the read head, the magnetic field either has the North or the South pole aligned first. Again, only two possible stages, North or South, 0 or 1. More on storage.

Page 1: What is the binary system
Page 2: The secrets of the binary system
Page 3: This page
Page 4: Bus width






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