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A+ Exam Prep: How Computers Measure and Transfer Data

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Understanding bytes and the other measurements derived from bytes is essential to choosing the correct sizes for RAM configurations, storage media, and much more. Some of the A+ Certification test questions typically deal with RAM and hard disk size measurements, as will your day-to-day work, so this chapter by Mark Soper will be especially helpful for the A+ exams and the real world.

In this chapter

  • Measurement: Bits, Bytes, and Beyond

  • Numbering Systems Used in Computers

  • Serial Versus Parallel Information Transfer

How do computers measure information? By the byte. It's the basic unit of measurement for all parts of the computer that involve the storage or management of information (RAM, storage, ROM). Here are a few examples:

  • Software stored on a floppy or hard disk occupies a finite number of bytes.

  • RAM is measured in megabytes (1MB = 1,000,000 bytes).

  • Drive capacity is measured in gigabytes (1GB = 1,000,000,000 bytes).

Understanding bytes and the other measurements derived from bytes is essential to choosing the correct sizes for RAM configurations, storage media, and much more. Some of the A+ Certification test questions typically deal with RAM and hard disk size measurements, as will your day-to-day work.

NOTE

The CD included with this book contains important Study Lab material for this chapter, as well as Chapters 2–22 in this book. The Study Lab for each chapter contains terms to study, exercises, and practice tests—all in printable PDF format (Adobe Acrobat Reader is included on the CD, too). These Study Lab materials will help you gear up for the A+ Exam. Also, the CD includes an industry-leading test engine from PrepLogic, which simulates the actual A+ test so that you can be sure that you're ready when test day arrives. Don't let the A+ test intimidate you. If you've read the chapters, worked through the Study Lab, and passed the practice tests from PrepLogic, you should be well prepared to ace the test!

Also, you'll notice that some words throughout each chapter are in bold format. These are study terms that are defined in the Study Lab. Be sure to consult the Study Lab when you are finished with this chapter to test what you've learned.

So, what's a byte? If you are storing text-only information in the computer, each character of that text (including spaces and punctuation marks) equals a byte. Thus, to calculate the number of bytes in the following sentence, count the letters, numbers, spaces, and punctuation marks:

"This book is written by Mark Edward Soper."
12345678901234567890123456789012345678901234
         |         |         |         |
        10        20        30        40

From this scale, you can see that the sentence uses 44 bytes. You can prove this to yourself by starting up Windows Notepad (or using MS-DOS's EDIT) and entering the text just as you see it printed here. Save the text as EXAMPLE.TXT and view the directory information (MS-DOS) or the File properties. You'll see that the text is exactly 44 bytes.

Do most computer programs store just the text when you write something? To find out, start up a word-processing program, such as Windows WordPad or Microsoft Word. Enter the same sentence again, and save it as EXAMPLE.If you use WordPad, save the file as a Rich Text Format (.RTF) file and as a Microsoft Word (.DOC) file. Depending upon the exact version of WordPad or Microsoft Word you use, the file takes up much more space. For example, WordPad for Windows XP saves text as an RTF file, using 243 bytes to store the file. The same sentence takes 19,968 bytes when saved as a .DOC file by Microsoft Word XP!

What happened? The next section explains this apparent oddity.

File Overhead and Other Features

When data you create is stored in a computer, it must be stored in a particular arrangement suitable for the program that created the information. This arrangement of information is called the file format.

A few programs, such as MS-DOS Edit and Windows Notepad, store only the text you create. What if you want to boldface a certain word in the text? A text-only editor can't do it. All that Edit and Notepad can store is text. As you have seen, in text-only storage, a character equals a byte.

In computer storage, however, pure text is seldom stored alone. WordPad and other word-processing programs such as Microsoft Word and Corel WordPerfect enable you to boldface, underline, italicize, and make text larger or smaller. You can also use different fonts in the same document (see Chapter 10, "Printers," for more about that).

Most modern programs also enable you to insert tables, create columns of text, and insert pictures into the text. Some, such as Microsoft Word, have provisions for tracking changes made by different users. In other words, there's a whole lot more than text in a document.

To keep all this non-text information arranged correctly with the text, WordPad and other programs must store references to these additional features along with the text, making even a sentence or two into a relatively large file, even if none of the extra features is actually used in that particular file. Thus, for most programs, the bytes used by the data they create is the total of the bytes used by the text or other information created by the program and the additional bytes needed to store the file in a particular file format.

Because different programs store data in different ways, it's possible to have an apparent software failure take place because a user tries to open a file made with program A with program B. Unless program B contains a converter that can understand and translate how program A stores data, program B can't read the file, and might even crash. To help avoid problems, Windows associates particular types of data files with matching programs, enabling you to open the file with the correct program by double-clicking the file in Explorer or File Manager. You'll learn more about file associations in Chapter 18, "Using and Optimizing Windows."

Numbering Systems Used in Computers

Three numbering systems are used in computers: decimal, binary, and hexadecimal. Decimal is also known as base 10. Binary is also known as base 2, and hexadecimal is also known as base 16. Here's an illustration to help you remember the basic differences between them.

You already are familiar with the decimal system: Look at your hands. Now, imagine your fingers are numbered from 0–9, for a total of 10 places. Decimal numbering is sometimes referred to as base 10.

The binary system doesn't use your fingers; instead, you count your hands: One hand represents 0, and the other 1, for a total of two places. Thus, binary numbering is sometimes referred to as base 2.

The hexadecimal system could be used by a pair of spiders who want to count: One spider's legs would be numbered 0–7, and the other spider's legs would be labeled 8, 9, A–F to reach a total of 16 places. Hexadecimal numbering is sometimes referred to as base 16.

TIP

Although all data in the computer is stored as a stream of binary values (0s and 1s), most of the time you will use decimal ("512MB of RAM") or hexadecimal ("memory conflict at C800 in upper memory") measurements. The typical rule of thumb is to use the system that produces the smallest meaningful number. If you need to convert between these systems, you can use any scientific calculator, including the Windows Calculator program (select View, Scientific from the menu).

Decimal Numbering System

We use the decimal or base 10 system for everyday math. A variation on straight decimal numbering is to use "powers of 2" as a shortcut for large values. For example, drive storage sizes often are defined in terms of decimal bytes, but the number of colors that a video card can display can be referred to as "24-bit" (or 224), which is the same as 16,777,216 colors.

Binary Numbering System

All data is stored in computers in a stream of 1s (on) and 0s (off). Because only two characters (0 and 1) are used to represent data, this is called a "binary" numbering system. Text is converted into its numerical equivalents before it is stored, so binary coding can be used to store all computer data and programs.

Table 3.1 shows how you would count from 1 to 10 (decimal) in binary.

Table 3.1 Decimal Numbers 1–10 and Binary Equivalents

Decimal

1

2

3

4

5

6

7

8

9

10

Binary

1

10

11

100

101

110

111

1000

1001

1010


Because even a small decimal number occupies many places if expressed in binary, binary numbers are usually converted into hexadecimal or decimal numbers for calculations or measurements.

TIP

Table 3.2 provides a listing of powers of 2, but you can use the Windows Calculator in scientific view mode to calculate any power of two you want. Just enter 2, click the x^y button, and enter the value for the power of 2 you want to calculate (such as 24). The results are displayed instantly (you add the commas). Use the Edit menu to copy the answer to the Windows Clipboard, and use your program's Paste command to bring it into your document. Sure beats counting on your fingers!

There are several ways to convert a decimal number into binary:

  • Use a scientific calculator with conversion.

  • Use the division method.

  • Use the subtraction method.

To use the division method

  1. Divide the number you want to convert by 2.

  2. Record the remainder: If there's no remainder, enter 0. If there's any remainder, enter 1.

  3. Divide the resulting answer by 2 again.

  4. Repeat the process, recording the remainder each time.

  5. Repeat the process until you divide 0 by 2. This is the last answer.

  6. When the last answer is divided, the binary is recorded from Least Significant Bit (LSB) to Most Significant Bit (MSB). Reverse the order of bit numbers so that MSB is recorded first and the conversion is complete. For example, to convert the decimal number 115 to binary using the division method, follow the procedure listed in Figure 3.1.

Figure 3.1Figure 3.1 Converting decimal 115 to binary with the division method.

If you use a scientific calculator (such as the scientific mode of the Windows Calculator) to perform the conversion, keep in mind that any leading zeros will be suppressed. For example, the calculation in Figure 3.1 indicates the binary equivalent of 115 decimal is 01110011. However, a scientific calculator will drop the leading zero and display the value as 1110011.

NOTE

Once you understand how binary numbering works, you can appreciate a joke going the rounds on the Internet and showing up on T-shirts near you:

"There are 10 kinds of people in the world—those who understand binary and those who don't." T-shirts are available from Think Geek (http://www.thinkgeek.com).

To use the subtraction method

  1. Look at the number you want to convert and determine the smallest power of 2 that is greater than or equal to the number you want to subtract. Table 3.2 lists powers of 2 from 20 through 217. For example, 115 decimal is less than 27 (128) but greater than 26 (64).

  2. Subtract the highest power of 2 from the value you want to convert. Record the value and write down binary 1.

  3. Move to the next lower power of 2. If you can subtract it, record the result and also write down binary 1. If you cannot subtract it, write down binary 0.

  4. Repeat step 3 until you attempt to subtract 20 (1). Again, write down binary 1 if you can subtract it, or binary 0 if you cannot. The binary values (0 and 1) you have recorded are the binary conversion for the decimal number. Unlike the division method, this method puts them in the correct order; there's no need to write them down in reverse order.

For example, to convert 115 decimal to binary using the subtraction method, see Figure 3.2.

Figure 3.2Figure 3.2 Converting 115 decimal to binary with the subtraction method.

Table 3.2 Powers of 2

Power of 2

Decimal Value

Power of 2

Decimal Value

20

1

29

512

21

2

210

1024

22

4

211

2048

23

8

212

4096

24

16

213

8192

25

32

214

16384

26

64

215

32768

27

128

216

65536

28

256

217

131072


Hexadecimal Numbering System

A third numbering system used in computers is hexadecimal. Hexadecimal numbering is also referred to as base 16, a convenient way to work with data because 16 is also the number of bits in 2 bytes or 4 nibbles. Hexadecimal numbers use the digits 0–9 and letters A–F to represent the 16 places (0–15 decimal). Hexadecimal numbers are used to represent locations in data storage, data access, and RAM. Table 3.3 shows how decimal numbers are represented in hex.

CAUTION

You might need to convert decimal to binary numbers for the A+ Certification exam, so try both pencil and paper methods (division and subtraction) and get comfortable with one of them.

Table 3.3 -Decimal and Hexadecimal Equivalents

Decimal

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

Hexadecimal

0

1

2

3

4

5

6

7

8

9

A

B

C

D

E

F


To convert decimal to hexadecimal, use the same division method listed previously, but use 16 rather than 2 as the divisor.

Figure 3.3 demonstrates how to use this conversion process to convert the decimal number of 65,536 (the start of upper memory) to its hexadecimal equivalent (A0000).

Figure 3.3Figure 3.3 Converting 65,536 decimal to hexadecimal.

Note that if you use the Windows Calculator in scientific mode to perform this conversion that you will get an answer of 100000. The initial value 10 is the numeric equivalent of hex A (refer to Table 3.3).

The most typical uses for hexadecimal numbering are

  • Upper memory addresses for add-on cards and for memory-management use

  • I/O port addresses for use with an add-on card

Binary Versus Decimal MB/GB

Although a byte represents the basic "building block" of storage and RAM calculation, most measurements are better performed with multiples of a byte. All calculations of the capacity of RAM and storage are done in bits and bytes. Eight bits is equal to one byte.

Table 3.4 provides the most typical values and their relationship to the byte.

Table 3.4 Decimal and Binary Measurements

Measurement

Number of Type*

Bytes/Bits

Calculations

Notes

Bit

 

1/8 of a byte

Byte/8

 

Nibble

 

1/2 of a byte

Byte/4 (4 bits)

 

Byte

 

8 bits

bit*8

 

Kilobit (Kb)

D

1,000 bits

 

 

Kibibit (Kib)

B

1,024 bits

 

1

 

 

(128 bytes)

 

 

Kilobyte (KB)

D

1,000 bytes

 

 

Kibibyte (KiB)

B

1,024 bytes

 

2

Megabit (Mb)

D

1,000,000 bits

1 kilobit2

 

Mebibit (Mib)

B

1,048,576 bits (131,072 bytes)

1 kibibit2

3

Megabyte (MB)

D

1,000,000 bytes

1,000KB

 

Mebibyte (MiB)

B

1,048,576 bytes (1,024KiB)

1 kilobyte2

4

Gigabit (Gb)

D

1,000,000,000 bits

1 kilobit3

 

Gibibit (Gib)

B

1,073,741,824 bits

1 kibibit3

5

Gigabyte (GB)

D

1,000,000,000 bytes

1 kilobyte3

 

Gibibyte (GiB)

B

1,073,741,824 bytes

1 kibibyte3

6


D=Decimal B=Binary

1Also known as binary kilobit

2Also known as binary kilobyte

3Also known as binary megabit

4Also known as binary megabyte

5Also known as binary gigabit

6Also known as binary gigabyte

Until December 1998, the terms kilobit, kilobyte, megabit, megabyte, gigabit, and gigabyte were officially used to refer both to decimal and binary values. A great deal of confusion in the industry has been caused by the indiscriminate use of both types of measurements for hard disk storage. Although the binary multiples shown in Table 3.4 are an IEC standard, many vendors in the computer business don't yet use the term kibibits or other binary multiples yet.

TIP

Because the industry has not yet widely adopted the terms kibi, mebi, and gibi, the A+ Certification Exam might use KB, MB, and GB to refer to either type of numbering system.

Floppy and hard disk manufacturers almost always rate their drives in decimal megabytes (multiples of 1 million bytes) or decimal gigabytes (multiples of 1 billion bytes), which is also the standard used by disk utilities, such as CHKDSK, ScanDisk, and FORMAT. However, most BIOSs and the MS-DOS/Windows FDISK and Windows NT/2000/XP Disk Management utilities list drive sizes in mebibytes (binary megabytes) or gibibytes (binary gigabytes). Mebibytes are also used to specify the size of rewritable and recordable CD and DVD media. Although the actual number of bytes is identical, the differences in numbering are confusing.

Take a hard disk rated by its maker as 8.4GB. This is 8,400,000,000 bytes (decimal). However, when the drive is detected and configured by the BIOS and partitioned with FDISK, its size is listed as only 7.82GB (binary GB—more accurately referred to as GiB). At first glance, you might believe you've lost some capacity (see Figure 3.4).

Figure 3.4Figure 3.4 The capacity of an 8.4GB hard disk size is 8.4 billion bytes (top bar), but most BIOSs and Windows FDISK/Disk Management measure drives in binary gigabytes (bottom bar).

However, as you've already seen, there is a substantial difference between the number of bytes in a binary gigabyte and one billion bytes. This different numbering system, not any loss of bytes, accounts for the seeming discrepancy. Use this information to help explain to a customer that the "missing" capacity of the hard disk isn't really missing (see Figure 3.5).

Figure 3.5Figure 3.5 A gibibyte (or binary gigabyte) has over 73 million more bytes than a decimal gigabyte (1 billion bytes).

Use the values in Table 3.4 to convert between decimal and binary values for drive sizes or other measurements. For the exam, keep in mind that values that can be divided by 1,000 are decimal, while values that can be divided by 1,024 are binary.

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