Bits, Bytes, and Measurement Terms 19
Binary Representation of Data
Computers are electromechanical devices made up of electronic switches. At the lowest
levels of computation, computers depend on these electronic switches to make decisions.
As such, computers react only to electrical impulses. These impulses are understood by
the computer as either on or off states (1s or 0s).
Computers work with and store data using electronic switches that are either on or off.
Computers can only understand and use data that is in this two-state (binary) format.
1 represents an on state, and 0 represents an off state. These 1s and 0s represent the
two possible states of an electronic component in a computer. These 1s and 0s are
called binary digits or bits.
The American Standard Code for Information Interchange (ASCII), the most com-
monly used code for representing alphanumeric data in a computer, uses binary digits
to represent the symbols typed on the keyboard. When computers send on/off states
over a network, electricity, light, or radio waves represent the 1s and 0s. Each charac-
ter has a unique pattern of eight binary digits assigned to represent the character.
Bits, Bytes, and Measurement Terms
Bits are binary digits. They are either 0s or 1s. In a computer, they are represented by
on/off switches or the presence or absence of electrical charges, light pulses, or radio
waves.
For example:
■ A binary 0 might be represented by 0 volts of electricity (0 = 0 volts).
■ A binary 1 might be represented by +5 volts of electricity (1 = +5 volts).
Computers are designed to use groupings of 8 bits. This grouping of 8 bits is called a
byte. In a computer, 1 byte represents a single addressable storage location. These stor-
age locations represent a value or a single character of data, such as an ASCII code.
The total number of combinations of the eight switches being turned on and off is 256
(or 2
8
). The value range of a byte is from 0 to 255. So, a byte is an important concept
to understand when working with computers and networks.

Most computer coding schemes use 8 bits to represent each number, letter, or symbol.
A series of 8 bits is called a byte; 1 byte represents a single addressable storage location
(see Table 1-2).
1102.book Page 19 Tuesday, May 20, 2003 2:53 PM
20 Chapter 1: Introduction to Networking
The following are commonly used computer measurement terms:
■ Bit—The smallest unit of data in a computer. A bit equals 1 or 0, and it is the
binary format in which data is processed, stored, and transmitted by computers.
■ Byte—A unit of measure used to describe the size of a data file, the amount of
space on a disk or another storage medium, or the amount of data being sent
over a network. 1 byte equals 8 bits of data.
■ Kb (kilobit)—Approximately 1000 bits.
■ KB (kilobyte)—Approximately 1000 bytes (1024 bytes exactly).
■ Mb (megabit)—Approximately 1 million bits.
■ MB (megabyte)—Approximately 1 million bytes (1,048,576 bytes exactly).
A megabyte is sometimes called a “meg.” The amount of RAM in most PCs is
typically measured in MB. Large files are often some number of MB in size.
■ GB (gigabyte)—Approximately 1 billion bytes. A gigabyte is sometimes called a
“gig.” Hard drive capacity on most PCs is typically measured in GB.
■ TB (terabyte)—Approximately 1 trillion bytes. Hard drive capacity on some
high-end computers is measured in TB.
■ kbps (kilobits per second)—One thousand bits per second. This is a standard
measurement of the amount of data transferred over a network connection.
■ kBps (kilobytes per second)—One thousand bytes per second. This is a standard
measurement of the amount of data transferred over a network connection.
Table 1-2 Units of Information
Unit Bytes
*
Bits
*

Bit (b) 1/8 byte 1 bit
Byte (B) 1 byte 8 bits
Kilobyte (KB) 1000 bytes 8000 bits
Megabyte (MB) 1 million bytes 8 million bits
Gigabyte (GB) 1 billion bytes 8 billion bits
Terabyte (TB) 1 trillion bytes 8 trillion bits
*
Common or approximate bytes or bits
N
O
TE
It is common to con-
fuse KB with Kb and
MB with Mb. Remem-
ber to do the proper
calculations when
comparing transmis-
sion speeds that are
measured in KB with
those measured in Kb.
For example, modem
software usually shows
the connection speed
in kilobits per second
(for example, 45 kbps).
However, popular
browsers display file-
download speeds in
kilobytes per second.
This means that with

a 45-kbps connec-
tion, the download
speed would be a
maximum of 5.76
kBps. In practice,
this download speed
cannot be reached
because of other fac-
tors that consume
bandwidth at the
same time. Also, file
sizes are typically
expressed in bytes,
whereas LAN band-
width and WAN
links are typically
expressed in kilobits
per second (kbps) or
Megabits per second
(Mbps). You must
multiply the number
of bytes in the file by
8 to determine the
amount of bandwidth
consumed in bps.
1102.book Page 20 Tuesday, May 20, 2003 2:53 PM
Bits, Bytes, and Measurement Terms 21
■ Mbps (megabits per second)—One million bits per second. This is a standard
measurement of the amount of data transferred over a network connection. Basic
Ethernet operates at 10 Mbps.

■ MBps (megabytes per second)—One million bytes per second. This is a standard
measurement of the amount of data transferred over a network connection.
■ Gbps (gigabits per second)—One billion bits per second. This is a standard mea-
surement of the amount of data transferred over a network connection. 10G or
10 Gigabit Ethernet operates at 10 Gbps.
■ Tbps (terabits per second)—One trillion bits per second. This is a standard mea-
surement of the amount of data transferred over a network connection. Some
high-speed core Internet routers and switches operate at more than Tbps.
■ Hz (hertz)—A unit of frequency. It is the rate of change in the state or cycle in a
sound wave, alternating current, or other cyclical waveform. It represents one
cycle per second.
■ MHz (megahertz)—One million cycles per second. This is a common measure-
ment of the speed of a processing chip, such as a computer microprocessor. Some
cordless phones operate in this range (for example, 900 MHz).
■ GHz (gigahertz)—One thousand million, or 1 billion (1,000,000,000), cycles per
second. This is a common measurement of the speed of a processing chip, such as
a computer microprocessor. Some cordless phones and wireless LANs operate in
this range (for example, 802.11b at 2.4 GHz).
Because computers are designed to work with on/off switches, binary digits and binary
numbers are natural to them. However, humans use the decimal number system in
their daily lives. It is hard to remember the long series of 1s and 0s that computers use.
Therefore, the computer’s binary numbers need to be converted to decimal numbers.
Sometimes, binary numbers need to be converted to hexadecimal (hex) numbers. This
is done because hex numbers can represent a long string of binary digits with just a
few hexadecimal digits. This makes it easier to remember and work with the numbers.
Base 10 Number System
A number system consists of symbols and rules for using those symbols. Many number
systems exist. The number system used most frequently is the decimal, or Base10,
number system. It is called Base10 because it uses ten symbols. These ten symbols are
the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Combinations of these digits can represent all

possible numeric values, as documented in Table 1-3.
NOTE
PC processors are get-
ting faster all the time.
The microprocessors
used in PCs in the
1980s typically ran at
less than 10 MHz (the
original IBM PC was
4.77 MHz). Currently,
PC processors are
pushing speeds up to
3 GHz, with faster
processors being devel-
oped for the future.
1102.book Page 21 Tuesday, May 20, 2003 2:53 PM
22 Chapter 1: Introduction to Networking
The decimal number system is based on powers of 10. The value of each column posi-
tion from right to left is multiplied by the number 10 (the base number) raised to a
power (exponent). The power that 10 is raised to depends on its position to the left
of the decimal point. When a decimal number is read from right to left, the first (right-
most) position represents 10
0
(1), and the second position represents 10
1
(10 ∗ 1 = 10).
The third position represents 10
2
(10 ∗ 10 = 100). The seventh position to the left rep-
resents 10

6
(10 × 10 ∗ 10 ∗ 10 ∗ 10 ∗ 10 = 1,000,000). This is true no matter how
many columns the number has.
For example:
2134 = (2 ∗ 10
3
) + (1 ∗ 10
2
) + (3 ∗ 10
1
) + (4 ∗ 10
0
)
There is a 4 in the ones position, a 3 in the tens position, a 1 in the hundreds position,
and a 2 in the thousands position. This example seems obvious when the decimal num-
ber system is used. Seeing exactly how the decimal system works is important, because
it is needed for you to understand two other number systems, binary (Base2) and hexa-
decimal (Base16). These systems use the same methods as the decimal system. Human-
readable IP addresses are expressed in Base10 (decimal). The IP address 172.16.14.188
is made up of four decimal numbers separated by dots or periods.
Base 2 Number System
Computers recognize and process data using the binary, or Base2, number system. The
binary number system uses only two symbols (0 and 1) instead of the ten symbols used
in the decimal, or Base10, number system. The position, or place, of each digit repre-
sents the number 2 (the base number) raised to a power (exponent) based on its posi-
tion (2
0
, 2
1
, 2

2
, 2
3
, 2
4
, and so on), as documented in Table 1-4.
Table 1-3 Base 10 Number System
Number of Symbols Ten
Symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Base Exponent
10
3
10
2
10
1
10
0
Place Value
1000 100 10 1
Example: 2,134
2 ∗10
3
1 ∗10
2
3 ∗10
1
4 ∗10
0
1102.book Page 22 Tuesday, May 20, 2003 2:53 PM

Bits, Bytes, and Measurement Terms 23
Example:
10110 = (1 ∗ 2
4
= 16) + (0 ∗ 2
3
= 0) + (1 ∗ 2
2
= 4) + (1 ∗ 2
1
= 2) + (0 ∗ 2
0
= 0)
= (16 + 0 + 4 + 2 + 0) = 22
If the binary number (10110) is read from left to right, there is a 1 in the 16s position,
a 0 in the 8s position, a 1 in the 4s position, a 1 in the 2s position, and a 0 in the 1s
position, which adds up to decimal number 22. Machine-readable IP addresses are
expressed as a string of 32 bits (binary).
Base 16 Number System
The Base16, or hexadecimal (hex), number system is used frequently when working
with computers because it can represent binary numbers in a more readable form. The
computer performs computations in binary, but there are several instances in which a
computer’s binary output is expressed in hexadecimal form to make it easier to read.
The hexadecimal number system uses 16 symbols. Combinations of these symbols can
represent all possible numbers. Because only ten symbols represent digits (0, 1, 2, 3, 4,
5, 6, 7, 8, and 9) and because Base16 requires six more symbols, the extra symbols are
the letters A, B, C, D, E, and F. The A represents the decimal number 10, B represents
11, C represents 12, D represents 13, E represents 14, and F represents 15, as shown in
Table 1-5.
The position of each symbol (digit) in a hex number represents the base number 16

raised to a power (exponent) based on its position. Moving from right to left, the first
position represents 16
0
(or 1), the second position represents 16
1
(or 16), the third
position represents 16
2
(or 256), and so on. Network adapter or NIC addresses are
expressed as a string of 12 hexadecimal characters.
Table 1-4 Base 2 Number System
Number of Symbols Two
Symbols 0, 1
Base Exponent
2
7
2
6
2
5
2
4
2
3
2
2
2
1
2
0

Place Value
1286432168421
Example: 10110
00010110
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24 Chapter 1: Introduction to Networking
Example:
1A2C = (1 ∗ 16
3
= 65536) + (10(A) ∗ 16
2
= 2560) + (2 ∗ 16
1
= 32) + (12(C) ∗ 16
0
= 12) = (65536 + 2560 + 32 + 12) = 68144
Decimal-to-Binary Conversion
You can convert decimal numbers to binary numbers in many different ways. The
flowchart shown in Figure 1-10 describes one method. This process involves trying to
figure out which values of the power of 2 are added together to get the decimal num-
ber being converted. This method is one of several that can be used. It is best to select
one method and practice with it until it always produces the correct answer.
Here’s an example:
These steps convert the decimal number 168 to binary:
Step 1 128 fits into 168, so the leftmost bit in the binary number is a 1.
168 – 128 = 40
Step 2 64 does not fit into 40, so the second bit from the left is a 0.
Step 3 32 fits into 40, so the third bit from the left is a 1.
40 – 32 = 8
Step 4 16 does not fit into 8, so the fourth bit from the left is a 0.

Step 5 8 fits into 8, so the fifth bit from the left is a 1.
8 – 8 = 0, so the remaining bits to the right are all 0s.
Step 6 As a result, the binary equivalent of the decimal value 168 is 10101000.
For more practice, try converting decimal 255 to binary. The answer should be
11111111.
Table 1-5 Base 16 Number System
Number of Symbols 16
Symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F
Base Exponent
16
3
16
2
16
1
16
0
Place Value
65536 256 16 1
Example: 1A2C
1A2C
1102.book Page 24 Tuesday, May 20, 2003 2:53 PM
Bits, Bytes, and Measurement Terms 25
Figure 1-10 Decimal-to-Binary Conversion Process
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26 Chapter 1: Introduction to Networking
This flowchart works for decimal numbers of 255 or less. It yields an eight-digit binary
number. This is appropriate for translating decimal IP addresses. Larger numbers can
be converted by starting with the highest power of 2 that fits. For example, the number
650 can be converted by first subtracting 512. This yields a ten-digit binary number.

Binary-to-Decimal Conversion
As with decimal-to-binary conversion, there is usually more than one way to solve the
conversion. The flowchart in Figure 1-11 shows one example.
Binary numbers can also be converted to decimal numbers by multiplying the binary
digits by the base number of the system (Base2) raised to the exponent of its position.
Here’s an example:
Convert the binary number 01110000 to a decimal number.
0 ∗ 2
0
= 0
+
0 ∗ 2
1
= 0
+
0 ∗ 2
2
= 0
+
0 ∗ 2
3
= 0
+
1 ∗ 2
4
= 16
+
1 ∗ 2
5
= 32

+
1 ∗ 2
6
= 64
+
0 ∗ 2
7
= 0
112
(The sum of the powers of 2 that have a 1 in their position)
Decimal-to-Binary Conversion
In this exercise, you practice converting decimal values to binary values.
N
O
TE
Work from right to
left. Remember that
anything raised to the
0 power is 1; there-
fore, 2
0
= 1.
1102.book Page 26 Tuesday, May 20, 2003 2:53 PM
Bits, Bytes, and Measurement Terms 27
Figure 1-11 Binary-to-Decimal Conversion Process
Start with
Binary Number.
Decimal
Total = 0
Total Now = Decimal

Stop
128 Bit = 1?
No Yes
Total = Total + 0
Total = Total + 128
64 Bit = 1?
No Yes
Total = Total + 0
Total = Total + 64
32 Bit = 1?
No Yes
Total = Total + 0
Total = Total + 32
16 Bit = 1?
No Yes
Total = Total + 0
Total = Total + 16
8 Bit = 1?
No Yes
Total = Total + 0
Total = Total + 8
4 Bit = 1?
No Yes
Total = Total + 0
Total = Total + 4
2 Bit = 1?
No Yes
Total = Total + 0
Total = Total + 2
1 Bit = 1?

No Yes
Total = Total + 0
Total = Total + 1
128 64 32 16 8 4 2 1
1102.book Page 27 Tuesday, May 20, 2003 2:53 PM
28 Chapter 1: Introduction to Networking
As with the flowchart shown in Figure 1-10, the flowchart shown in Figure 1-11 also
works for decimal numbers of 255 or less that start with an eight-digit binary number.
Larger binary numbers can be converted by increasing the power of 2 for each bit on
the right. For example, if you have a ten-digit binary number, the tenth digit is worth
512, and the ninth is worth 256 if they are turned on (have a value of 1).
Hexadecimal and Binary Conversion
Converting a hexadecimal number to binary form and vice versa is a common task
when dealing with the configuration register in Cisco routers. Cisco routers have a
configuration register that is 16 bits long. That 16-bit binary number can be repre-
sented as a four-digit hexadecimal number. For example, 0010000100000010 in
binary equals 2102 in hex.
Layer 2 Media Access Control (MAC) addresses are typically written in hex. For
Ethernet and Token Ring, these addresses are 48 bits, or six
octets (one octet is 1 byte).
(“Oct” comes from the Greek word for eight.) Because these addresses consist of six
distinct octets, they can be expressed as 12 hex numbers instead. Every 4 bits is a hex
digit (2
4
= 16), as you will see in Table 1-6 in a moment.
Instead of writing
10101010.11110000.11000001.11100010.01110111.01010001
you can write the much-shorter hex equivalent:
AA.F0.C1.E2.77.51.
To make handling hex versions of MAC addresses even easier, the dots are placed only

after every four hex digits, as in AAF0.C1E2.7751.
The most common way for computers and software to express hexadecimal output is
by using 0x in front of the hexadecimal number. Thus, whenever you see 0x, you know
that the number that follows is a hexadecimal number. For example, 0x1234 means
1234 in base 16.
Like the binary and decimal number systems, the hexadecimal system is based on the
use of symbols, powers, and positions. The symbols that hex uses are 0 through 9 and
A through F. Table 1-6 shows the binary and decimal equivalents of hex digits.
Binary-to-Decimal Conversion
In this exercise, you practice converting binary values to decimal values.
1102.book Page 28 Tuesday, May 20, 2003 2:53 PM