Help Desk.How It Works.Page Two

Help: How it Works: 2 of 9

Bits, Bytes and Binary Numbers

Since you probably don't remember anything about Binary numbers from your junior high studies, let's all take a quick refresher course.

Most of us would say that the number 1101 represents "One thousand, one hundred and one." In our "Base-10" system, the first space (on the right) is the "Ones" column. Moving to the left, we find the "Tens," Hundreds," and "Thousands" columns. Each column represents a value that is TEN times the value of the column to its right. And, we can place any number from 0-9 in each column.

But, in the "Base-2" Binary system, the only "numbers" we can place in each column are "0" and "1," and each column represents a value that is only TWO times the value of the column to its right. So, as we read from right to left, the number 1101 would be read as: 1 in the "Ones" column, 0 in the "Twos" column, 1 in the "Fours" column, and 1 in the "Eights" column. If we add those values together (8+4+0+1), we see that the Binary number 1101 represents the "Base-10" value we call 13.

Why don't computers use the Base-10 system? Because each magnetic particle on a disk drive, and each transistor inside the RAM or CPU, is like a tiny switch with only two possible values. "Charged" or "On" represents a value of ONE (1). "Off" or "Without Charge" represents a value of ZERO (0). When these electronic or magnetic switches are used to define data, we call each of them a "bit." And, to move them around efficiently inside the computer, we lump them together in groups of eight that we call a "Byte." (1 Byte = 8 bits.)

Now, here's the really important part. Using the Binary system, the eight "switches" in each Byte can be arranged in 256 different combinations to represent 256 different values, ranging from from Zero (00000000) up to 255 (11111111). As you read through this "How It Works" area, you'll see again and again that 256 is a "magic" number.

Bigger Bunches of Bytes

Of course, one data Byte doesn't amount to much. (In a word processing document, for example, one byte of data is required to represent each of the individual alphabetic characters.) To help keep track of the billions of data bytes which are constantly moving around inside your machine, we usually lump them together into larger, more manageable groups. One example is the Kilobyte (K).

If you know Latin (kilo = thousand), you might assume that one Kilobyte equals 1,000 bytes. Not exactly. Because computers use the Binary system, everything is counted as a "power of 2." The closest we can get to the Base-10 number "1,000" using the binary numbering system is "2 to the 10th power" (2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 ) or 1,024. So, one Kilobyte actually equals 1,024 Bytes of data.

The same basic equation is used to define even larger chunks of data, like the Megabyte (MB) or the Gigabyte (GB).

1 MB = 1,024 K = 1,048,576 Bytes
1 GB = 1,024 MB = 1,048,576 K = 1,073,741,824 Bytes

How are these numbers used in the real world? Well, a floppy disk can hold about 1.44 MB (1.44 million bytes) of data. CD-ROM disks can hold roughly 640 MB (640 million bytes). And a modern hard disk drive might hold more than 4 Gigabytes (4 BILLION bytes) of data. (NOTE: The largest measure of data currently being used is the "Terabyte." One Terabyte equals 1,024 Gigabytes - roughly ONE TRILLION bytes of data.)

These days, most documents are measured in Kilobytes (K), RAM modules are measured in Megabytes (MB), and Hard Disk Drives are almost always measured in Gigabytes (GB). But, there are still one or two less common computer statistics where you'll need to know the difference between bits and bytes.

One example is the "width" of the "Data Path" used in the computer's "System Bus" (The main internal pathway between components). This figure defines the number of data BITS contained in each data "chunk" moving around inside your computer. The original Macs used a 16-bit (2-Byte) data path. Many Wintel PC's still use a 32-bit (4-Byte) data path. But, all of today's PowerMacs move data using a 64-bit (8-Byte) data path, so they perform much faster.

You will also need to know the difference between bits and bytes when dealing with monitors, VRAM and graphics accelerators, deciding what type of "addressing" you should use for your hard drive and RAM, and when selecting modems. We'll talk more about each of these subjects on other pages in this section.

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Help: How it Works: 2 of 9
Bits, Bytes and Binary Numbers Since you probably don't remember anything about Binary numbers from your junior high studies, let's all take a quick refresher course. Most of us would say that the number 1101 represents "One thousand, one hundred and one." In our "Base-10" system, the first space (on the right) is the "Ones" column. Moving to the left, we find the "Tens," Hundreds," and "Thousands" columns. Each column represents a value that is TEN times the value of the column to its right. And, we can place any number from 0-9 in each column. But, in the "Base-2" Binary system, the only "numbers" we can place in each column are "0" and "1," and each column represents a value that is only TWO times the value of the column to its right. So, as we read from right to left, the number 1101 would be read as: 1 in the "Ones" column, 0 in the "Twos" column, 1 in the "Fours" column, and 1 in the "Eights" column. If we add those values together (8+4+0+1), we see that the Binary number 1101 represents the "Base-10" value we call 13. Why don't computers use the Base-10 system? Because each magnetic particle on a disk drive, and each transistor inside the RAM or CPU, is like a tiny switch with only two possible values. "Charged" or "On" represents a value of ONE (1). "Off" or "Without Charge" represents a value of ZERO (0). When these electronic or magnetic switches are used to define data, we call each of them a "bit." And, to move them around efficiently inside the computer, we lump them together in groups of eight that we call a "Byte." (1 Byte = 8 bits.) Now, here's the really important part. Using the Binary system, the eight "switches" in each Byte can be arranged in 256 different combinations to represent 256 different values, ranging from from Zero (00000000) up to 255 (11111111). As you read through this "How It Works" area, you'll see again and again that 256 is a "magic" number. Bigger Bunches of Bytes Of course, one data Byte doesn't amount to much. (In a word processing document, for example, one byte of data is required to represent each of the individual alphabetic characters.) To help keep track of the billions of data bytes which are constantly moving around inside your machine, we usually lump them together into larger, more manageable groups. One example is the Kilobyte (K). If you know Latin (kilo = thousand), you might assume that one Kilobyte equals 1,000 bytes. Not exactly. Because computers use the Binary system, everything is counted as a "power of 2." The closest we can get to the Base-10 number "1,000" using the binary numbering system is "2 to the 10th power" (2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 ) or 1,024. So, one Kilobyte actually equals 1,024 Bytes of data. The same basic equation is used to define even larger chunks of data, like the Megabyte (MB) or the Gigabyte (GB). 1 MB = 1,024 K = 1,048,576 Bytes 1 GB = 1,024 MB = 1,048,576 K = 1,073,741,824 Bytes How are these numbers used in the real world? Well, a floppy disk can hold about 1.44 MB (1.44 million bytes) of data. CD-ROM disks can hold roughly 640 MB (640 million bytes). And a modern hard disk drive might hold more than 4 Gigabytes (4 BILLION bytes) of data. (NOTE: The largest measure of data currently being used is the "Terabyte." One Terabyte equals 1,024 Gigabytes - roughly ONE TRILLION bytes of data.) These days, most documents are measured in Kilobytes (K), RAM modules are measured in Megabytes (MB), and Hard Disk Drives are almost always measured in Gigabytes (GB). But, there are still one or two less common computer statistics where you'll need to know the difference between bits and bytes. One example is the "width" of the "Data Path" used in the computer's "System Bus" (The main internal pathway between components). This figure defines the number of data BITS contained in each data "chunk" moving around inside your computer. The original Macs used a 16-bit (2-Byte) data path. Many Wintel PC's still use a 32-bit (4-Byte) data path. But, all of today's PowerMacs move data using a 64-bit (8-Byte) data path, so they perform much faster. You will also need to know the difference between bits and bytes when dealing with monitors, VRAM and graphics accelerators, deciding what type of "addressing" you should use for your hard drive and RAM, and when selecting modems. We'll talk more about each of these subjects on other pages in this section.
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HOME . SERVICES . HELP DESK . RESOURCES . WHY MAC . CREDENTIALS
Copyright 1998, 5-Minute Mac Consulting, Wampum, Pennsylvania, USA