Lab 1: Conversion between different number systems
1.1 Decimal to Binary Conversion
Objective
Learn to convert decimal values to binary values.
Practice converting decimal values to binary values.
Background
Knowing how to convert decimal values to binary values is valuable when converting human readable IP
addresses in dotted decimal format to machine-readable binary format. This is normally done for calculation of subnet
masks and other tasks. The following is an example of an IP address in 32-bit binary form and dotted decimal form.
Binary IP Address:
11000000.10101000.00101101.01111001
Decimal IP Address: 192.168.45.121
A tool that makes the conversion of decimal values to binary values simple is the following table. The first row
is created by counting right to left from one to eight, for the basic eight bit positions. The table will work for
any size binary value. The value row starts with one and doubles, Base 2, for each position to the left.
Position
8
7
6
5
4
3
2
1
128
64
32
16
8
4
2
1
Value
128 207
64
8
4
2
The same conversion table and simple division can be used to convert binary values to decimal values.
Steps
To convert 207 to binary:
1.
Start with the digit farthest to the left. Determine if the decimal value can be divided by it. Since it will go
one time, put a 1 in row three of the conversion table under the 128 value and calculate the remainder, 79.
2.
Since the remainder can be divided by the next value, 64, put a 1 in row three under the
64 value of the table.
3.
Since the remainder cannot be divided by either 32 or 16, put 0s in row three of our table
under the 32 and 16 values.
4.
Continue until there is no remainder.
5.
If necessary, use row four to check the work.
Position
Value
8
7
6
5
4
3
2
1
128
64
32
16
8
4
2
1
1
1
0
0
1
1
1
1
128
64
8
4
2
1
= 207
6.
Convert the following decimal values to binary values:
a. 123 __01111011_____________________
b. 202 _____11001010__________________
c. 67 _____0100 0011__________________
d. 7 _______0111________________
e. 252 _________11111100______________
f. 91 _____________01011011__________
g. 116.127.71.3 ____01110100________ ____0111111________ _____01000111_______
_____0011_______
h. 255.255.255.0 _____11111111_______ ______11111111______ ____________
_____00000000_______
i. 192.143.255.255 ______11000000______ ______10001111______
_____11111111_______ _____11111111_______
j. 12.101.9.16 ______00001100______ ____01100101________ _____00001001_______
_____00010000_______
This concludes the lab.
1.2 Binary to Decimal Conversion
Objective
Learn the process of converting binary values to decimal
values.
Practice converting binary values to decimal values.
Background
The following is an example of an IP address in 32-bit binary form and dotted decimal form.
Binary IP Address:
11000000.10101000.00101101.01111001
Decimal IP Address: 192.168.45.121
Binary data is made up of ones and zeros. Ones represent on and zeros represent off. Binary data can be
grouped in varying increments, 110 or 1011. In TCP/IP binary data is usually grouped in
eight digit groups called a Byte.
A Byte, 8 bits, can range from 00000000 to 11111111 creating 256 combinations with decimal values ranging
from 0 to 255. IP addressing uses 4 bytes, or 32 bits, to identify both the network and specific device. The
specific device can be a node or host. The example at the beginning of this
lab is an example of an IP address in both binary decimal formats.
A tool that makes the conversion of binary to decimal values simple is the following table. The first row is
created by counting right to left from one to eight for the basic eight bit positions. The tale will work for any size binary
value. The value row starts
with one and doubles,
base 2, for each position to the
8
7
6
5
4
3
2
1 left.
Position
Value
128
64
32
16
8
Steps
1.
Enter the binary bits in row three. For example 10111001
4
2
1
2.
Put the decimal values in row four only for the third row 1s. Technically the row two values are being
multiplied by row three.
3.
Now just add row four across.
Position
Value
8
7
6
5
4
3
2
1
128
64
32
16
8
4
2
1
1
0
1
1
1
0
0
1
32
16
8
128
4.
1
Convert the following binary values to decimals:
a. 1110 ________14_______________
b. 100110 _______38________________
c. 11111111
_______255________________
d. 11010011
________211_______________
e. 01000001
________65_______________
f. 11001110
________206_______________
g. 01110101
_________117______________
h. 10001111
__________143_____________
i. 11101001.00011011.10000000.10100100
_________233________ _______27__________ ________128_________
__________164_______
j. 10101010.00110100.11100110.00010111
________170_________ _______52__________ ______230___________
________23_________
1.3 Hexadecimal Conversions
Objective
= 185
Learn the process to convert hexadecimal values to decimal and
binary
values.
Learn the process to convert decimal and binary values to
hexadecimal values.
Practice converting between decimal, binary and hexadecimal values.
Background / Preparation
The Hexadecimal (Hex) number system is used to refer to the binary numbers in a
NIC or IPv6 address. The word hexadecimal comes from the Greek word for 16.
Hexadecimal is often abbreviated "0x", zero and lower case x. Hex numbers use 16
unique digits to display any
Dec
Hex
Binary
0
0
0000
1
1
0001
combination of eight binary digits as only two hexadecimal digits.
2
2
0010
A Byte, or 8 bits, can range from 00000000 to 11111111. A Byte can create 256
combinations with decimal values ranging from 0 to 255 or Hex values 0 to FF. Each Hex
value represents only four binary bits. The alpha
(A-F) values are not case sensitive.
3
3
0011
4
4
0100
A tool that makes the conversion of hexadecimal to decimal values simple is the
following table. Use the same techniques as covered in binary to decimal conversions. The
first row is the two Hex positions. The
value row starts as 1 and 16, base 16, for each
position to the left.
5
5
0101
6
6
0110
7
7
0111
8
8
1000
9
9
1001
10
A
1010
11
B
1011
12
C
1100
13
D
1101
14
E
1110
15
F
1111
Position
Value
2
16
1
1
Note: Steps are provided at the end of this lab in the use of the Windows Scientific
Calculator to check the work.
Steps for Hex to decimal conversion
1.
Break the Hex value into pairs. Start at the right side. For example 77CE becomes 77 and CE. Insert a zero
in the first position if necessary to complete the first pair.
2.
Put each Hex pair in row three. The value in parenthesis is the decimal value of A-F.
3.
To get the decimal values in row four, multiply the row two values by row three.
4.
Now just add row four across.
Position
2
1
Value
16
1
7
7
112
7
= 119
Position
2
1
Value
16
1
C(12)
E(14)
192
14
= 206
Steps for decimal to Hex conversion
1.
To be valid for the purpose of this lab, the decimal value will be between 0 and 256. The first Hex value is
derived by dividing the decimal value by 16. If the value is greater than 9 it will need to be put in Hex form
A-F.
2.
The second value is the remainder from step 1. If the value is greater than 9 it will need to be put in Hex
form A-F.
3.
For example, 209 divided by 16 is 13 with a remainder of 1. 13 equals D in Hex. Therefore, 209 equals D1.
Steps for Hex to binary conversion
1.
This is the easiest conversion. Remember that each Hex value converts to four binary bits, so work right
to left.
2.
For example, to convert 77AE to binary. Start with E. Use the table at the beginning of this lab to go
directly to binary. The other alternative is to convert the value to decimal, E = 14, and then use the last
four positions of the table used in the decimal to binary conversions.
14 divided by 8 is 1 with a remainder of
6. 6 divided by 4 is 1 with a remainder of 2. 2
divided by 2 is 1 with no remainder.
Add zeros if necessary to end up with four bits.
Position
4
3
2
1
8
4
2
1
1
1
1
0
8
4
2
Value
= 14
3.
Using the same technique, A becomes 1010 and the total so far is 10101110.
Position
Value
= 10
4
3
2
1
8
4
2
1
1
0
1
0
8
4.
2
Using the same technique, the two 7s each become 0111 and the total is 01110111.10101110.
Position
Value
4
3
2
1
8
4
2
1
0
1
1
1
4
2
1
=7
Steps for binary to Hex conversion
1.
Each Hex value equals four binary bits. Start by breaking the binary value into 4-bit units from right to left. Add
any leading zeros required to end up with all 4-bit values. 01101110.
11101100 would become 0110 1110 1110 1100.
2.
Use the table at the beginning of this lab to go directly to Hex. The other alternative is to convert each 4-bit
binary value to decimal, 0-15. Then convert the decimal to Hex, 0-F.
4
3
2
1
8
4
2
1
1
1
0
0
8
4
Position
4
3
2
1
Value
8
4
2
1
1
1
1
0
8
4
2
Position
Value
= 12 or C
= 14 or E
3. The result is 6E-EC.
Practice
Convert the following values to the other two forms:
Decimal
Hex
Binary
1
169
a9
10101001
2
255
FF
11111111
3
47825
Bad1
1011101011010001
4
231-99-28
E7-63-1C
11100111-01100011-00011100
5
53
35
00110101
6
115
73
01110011
7
19
13
00010011
8
212.65.119.45
D4.41.77.2D 11010100.01000001.01110111.00101101
9
170
AA
10101010
1.4 Converting IPv4 Addresses to Binary
Objectives
Part 1: Convert IPv4 Addresses from Dotted Decimal to Binary
Part 2: Use Bitwise ANDing Operation to Determine Network Addresses
Part 3: Apply Network Address Calculations
Scenario
Every IPv4 address is comprised of two parts: a network portion and a host portion. The network portion of an address is
the same for all devices that reside in the same network. The host portion identifies a specific host within a given network.
The subnet mask is used to determine the network portion of an IP address. Devices on the same network can
communicate directly; devices on different networks require an intermediary Layer 3 device, such as a router, to
communicate.
To understand the operation of devices on a network, we need to look at addresses the way devices do in binary
notation. To do this, we must convert the dotted decimal form of an IP address and its subnet mask to binary notation.
After this has been done, we can use the bitwise ANDing operation to determine the network address.
This lab provides instructions on how to determine the network and host portion of IP addresses by converting addresses
and subnet masks from dotted decimal to binary, and then using the bitwise ANDing operation. You will then apply this
information to identify addresses in the network.
Part 1: Convert IPv4 Addresses from Dotted Decimal to Binary
In Part 1, you will convert decimal numbers to their binary equivalent. After you have mastered this activity, you will
convert IPv4 addresses and subnet masks from dotted decimal to their binary form.
Step 1: Convert decimal numbers to their binary equivalent.
Fill in the following table by converting the decimal number to an 8-bit binary number. The first number has been
completed for your reference. Recall that the eight binary bit values in an octet are based on the powers of 2, and from left
to right are 128, 64, 32, 16, 8, 4, 2, and 1.
Decimal
Binary
192
11000000
168
10101000
10
1010
255
11111111
2
00000010
Step 2: Convert the IPv4 addresses to their binary equivalent.
An IPv4 address can be converted using the same technique you used above. Fill in the table below with the binary
equivalent of the addresses provided. To make your answers easier to read, separate the binary octets with a period.
Decimal
192.168.10.10
Binary
11000000.10101000.00001010.00001010
209.165.200.229
11010001.10100101.11001000.11100101
172.16.18.183
10101100.00010000.00010010.10110111
10.86.252.17
00001010.01010110.11111100.00010001
255.255.255.128
11111111.11111111.11111111.10000000
255.255.192.0
11111111.11111111.11000000.00000000
Part 2: Use Bitwise ANDing Operation to Determine Network Addresses
In Part 2, you will use the bitwise ANDing operation to calculate the network address for the provided host addresses.
You will first need to convert an IPv4 decimal address and subnet mask to their binary equivalent. Once you have the
binary form of the network address, convert it to its decimal form.
Note: The ANDing process compares the binary value in each bit position of the 32-bit host IP with the corresponding
position in the 32-bit subnet mask. If there two 0s or a 0 and a 1, the ANDing result is 0. If there are two 1s, the result is
a 1, as shown in the example here.
Step 1: Determine the number of bits to use to calculate the network address.
Description
Decimal
Binary
IP Address
192.168.10.131
11000000.10101000.00001010.10000011
Subnet Mask
255.255.255.192
11111111.11111111.11111111.11000000
Network Address
192.168.10.128
11000000.10101000.00001010.10000000
How do you determine what bits to use to calculate the network address?
___We convert IP Address and subnet mask to binary.
In the example above, how many bits are used to calculate the network address?
__32 Bits__________________________________________________________________________________
Step 2: Use the ANDing operation to determine the network address.
a.
Enter the missing information into the table below:
Description
b.
172.16.145.29
10101100.00010000.10010001.00011101
Subnet Mask
255.255.0.0
11111111.11111111.00000000.00000000
Network Address
172.16.0.0
10101100.00010000.00000000.00000000
Enter the missing information into the table below:
Binary
192.168.10.10
11000000.10101000.00001010.00001010
Subnet Mask
255.255.255.0
11111111.11111111.11111111.00000000
Network Address
192.168.10.0
11000000.10101000.00001010.00000000
Enter the missing information into the table below:
Decimal
Binary
IP Address
192.168.68.210
11000000.10101000.01000100.11010010
Subnet Mask
255.255.255.128
11111111.11111111.11111111.10000000
Network Address
192.168.68.64
11000000.10101000.01000100.10000000
Enter the missing information into the table below:
Description
e.
Decimal
IP Address
Description
d.
Binary
IP Address
Description
c.
Decimal
Decimal
Binary
IP Address
172.16.188.15
10101100.00010000.10111100.00001111
Subnet Mask
255.255.240.0
11111111.11111111.11110000.00000000
Network Address
172.16.176.0
10101100.00010000.10110000.00000000
Enter the missing information into the table below:
Description
Decimal
Binary
IP Address
10.172.2.8
00001010.10101100.00000010.00001000
Subnet Mask
255.224.0.0
11111111.11100000.00000000.00000000
Network Address
10.160.0.0
00001010.10100000.00000000.00000000
Part 3: Apply Network Address Calculations
In Part 3, you must calculate the network address for the given IP addresses and subnet masks. After you have the
network address, you should be able to determine the responses needed to complete the lab.
Step 1: Determine whether IP addresses are on same network.
a.
You are configuring two PCs for your network. PC-A is given an IP address of 192.168.1.18, and PC-B is given an
IP address of 192.168.1.33. Both PCs receive a subnet mask of 255.255.255.240.
What is the network address for PC-A? ___________________________
What is the network address for PC-B? ___________________________
Will these PCs be able to communicate directly with each other? _______
What is the highest address that can be given to PC-B that allows it to be on the same network as PC-A?
___________________________
b.
You are configuring two PCs for your network. PC-A is given an IP address of 10.0.0.16, and PC-B is given an IP
address of 10.1.14.68. Both PCs receive a subnet mask of 255.254.0.0.
What is the network address for PC-A? __________________________
What is the network address for PC-B? __________________________
Will these PCs be able to communicate directly with each other? ______
What is the lowest address that can be given to PC-B that allows it to be on the same network as PC-A?
___________________________
Step 2: Identify the default gateway address.
a.
Your company has a policy to use the first IP address in a network as the default gateway address. A host on the
local-area network (LAN) has an IP address of 172.16.140.24 and a subnet mask of 255.255.192.0.
What is the network address for this network?
___________________________
What is the default gateway address for this host?
___________________________
b.
Your company has a policy to use the first IP address in a network as the default gateway address. You have been
instructed to configure a new server with an IP address of 192.168.184.227 and a subnet mask of 255.255.255.248.
What is the network address for this network?
___________________________
What is the default gateway for this server?
___________________________