Question

IP address is: 203.120.45.23 and subnet mask is: 255.255.255.240. Represent this information in CIDR format. IP address for Device-A is: 172.255.20.30/20 and Device-B is: 172.255.14.30/20. Are these devices on the same subnet or on different subnets? Find out the network address for each of the devices

Answer 1

1)
Let's convert this into binary format
255.255.255.240
Let's convert all octets to binary separately
Converting 255 to binary
Divide 255 successively by 2 until the quotient is 0
   > 255/2 = 127, remainder is 1
   > 127/2 = 63, remainder is 1
   > 63/2 = 31, remainder is 1
   > 31/2 = 15, remainder is 1
   > 15/2 = 7, remainder is 1
   > 7/2 = 3, remainder is 1
   > 3/2 = 1, remainder is 1
   > 1/2 = 0, remainder is 1
Read remainders from the bottom to top as 11111111
So, 255 of decimal is 11111111 in binary
255 in binary is 11111111

Converting 255 to binary
Divide 255 successively by 2 until the quotient is 0
   > 255/2 = 127, remainder is 1
   > 127/2 = 63, remainder is 1
   > 63/2 = 31, remainder is 1
   > 31/2 = 15, remainder is 1
   > 15/2 = 7, remainder is 1
   > 7/2 = 3, remainder is 1
   > 3/2 = 1, remainder is 1
   > 1/2 = 0, remainder is 1
Read remainders from the bottom to top as 11111111
So, 255 of decimal is 11111111 in binary
255 in binary is 11111111

Converting 255 to binary
Divide 255 successively by 2 until the quotient is 0
   > 255/2 = 127, remainder is 1
   > 127/2 = 63, remainder is 1
   > 63/2 = 31, remainder is 1
   > 31/2 = 15, remainder is 1
   > 15/2 = 7, remainder is 1
   > 7/2 = 3, remainder is 1
   > 3/2 = 1, remainder is 1
   > 1/2 = 0, remainder is 1
Read remainders from the bottom to top as 11111111
So, 255 of decimal is 11111111 in binary
255 in binary is 11111111

Converting 240 to binary
Divide 240 successively by 2 until the quotient is 0
   > 240/2 = 120, remainder is 0
   > 120/2 = 60, remainder is 0
   > 60/2 = 30, remainder is 0
   > 30/2 = 15, remainder is 0
   > 15/2 = 7, remainder is 1
   > 7/2 = 3, remainder is 1
   > 3/2 = 1, remainder is 1
   > 1/2 = 0, remainder is 1
Read remainders from the bottom to top as 11110000
So, 240 of decimal is 11110000 in binary
240 in binary is 11110000

======================================================================================
||    255.255.255.240 in binary notation is 11111111.11111111.11111111.11110000    ||
======================================================================================

Remove all dots to form 11111111111111111111111111110000
Remove all 0's from the right side to form 1111111111111111111111111111
Number of 1's in this is 28
so, Subnet mask is /28

Answer:
--------
203.120.45.23/28

2)
IP Address: 172.255.20.30
----------------------------------------
Let's first convert this into binary format
172.255.20.30
Let's convert all octets to binary separately
Converting 172 to binary
Divide 172 successively by 2 until the quotient is 0
   > 172/2 = 86, remainder is 0
   > 86/2 = 43, remainder is 0
   > 43/2 = 21, remainder is 1
   > 21/2 = 10, remainder is 1
   > 10/2 = 5, remainder is 0
   > 5/2 = 2, remainder is 1
   > 2/2 = 1, remainder is 0
   > 1/2 = 0, remainder is 1
Read remainders from the bottom to top as 10101100
So, 172 of decimal is 10101100 in binary
172 in binary is 10101100

Converting 255 to binary
Divide 255 successively by 2 until the quotient is 0
   > 255/2 = 127, remainder is 1
   > 127/2 = 63, remainder is 1
   > 63/2 = 31, remainder is 1
   > 31/2 = 15, remainder is 1
   > 15/2 = 7, remainder is 1
   > 7/2 = 3, remainder is 1
   > 3/2 = 1, remainder is 1
   > 1/2 = 0, remainder is 1
Read remainders from the bottom to top as 11111111
So, 255 of decimal is 11111111 in binary
255 in binary is 11111111

Converting 20 to binary
Divide 20 successively by 2 until the quotient is 0
   > 20/2 = 10, remainder is 0
   > 10/2 = 5, remainder is 0
   > 5/2 = 2, remainder is 1
   > 2/2 = 1, remainder is 0
   > 1/2 = 0, remainder is 1
Read remainders from the bottom to top as 10100
So, 20 of decimal is 10100 in binary
20 in binary is 00010100

Converting 30 to binary
Divide 30 successively by 2 until the quotient is 0
   > 30/2 = 15, remainder is 0
   > 15/2 = 7, remainder is 1
   > 7/2 = 3, remainder is 1
   > 3/2 = 1, remainder is 1
   > 1/2 = 0, remainder is 1
Read remainders from the bottom to top as 11110
So, 30 of decimal is 11110 in binary
30 in binary is 00011110

====================================================================================
||    172.255.20.30 in binary notation is 10101100.11111111.00010100.00011110    ||
====================================================================================

Subnet mask is /20

For Calculating network ID, keep first 20 bits of 10101100.11111111.00010100.00011110 and set all remaining bits to 0.
so, network ID in binary is 10101100.11111111.00010000.00000000
10101100.11111111.00010000.00000000:
----------------------------------------
10101100.11111111.00010000.00000000
Let's convert all octets to decimal separately
Converting 10101100 to decimal
=> 10101100
=> 1x2^7+0x2^6+1x2^5+0x2^4+1x2^3+1x2^2+0x2^1+0x2^0
=> 1x128+0x64+1x32+0x16+1x8+1x4+0x2+0x1
=> 128+0+32+0+8+4+0+0
=> 172
10101100 in decimal is 172

Converting 11111111 to decimal
=> 11111111
=> 1x2^7+1x2^6+1x2^5+1x2^4+1x2^3+1x2^2+1x2^1+1x2^0
=> 1x128+1x64+1x32+1x16+1x8+1x4+1x2+1x1
=> 128+64+32+16+8+4+2+1
=> 255
11111111 in decimal is 255

Converting 00010000 to decimal
=> 00010000
=> 0x2^7+0x2^6+0x2^5+1x2^4+0x2^3+0x2^2+0x2^1+0x2^0
=> 0x128+0x64+0x32+1x16+0x8+0x4+0x2+0x1
=> 0+0+0+16+0+0+0+0
=> 16
00010000 in decimal is 16

Converting 00000000 to decimal
=> 00000000
=> 0x2^7+0x2^6+0x2^5+0x2^4+0x2^3+0x2^2+0x2^1+0x2^0
=> 0x128+0x64+0x32+0x16+0x8+0x4+0x2+0x1
=> 0+0+0+0+0+0+0+0
=> 0
00000000 in decimal is 0

====================================================================================
||    10101100.11111111.00010000.00000000 in decimal notation is 172.255.16.0    ||
====================================================================================
===========================================
||    So, Network ID is 172.255.16.0    ||
===========================================

IP Address: 172.255.14.30
----------------------------------------
Let's first convert this into binary format
172.255.14.30
Let's convert all octets to binary separately
Converting 172 to binary
Divide 172 successively by 2 until the quotient is 0
   > 172/2 = 86, remainder is 0
   > 86/2 = 43, remainder is 0
   > 43/2 = 21, remainder is 1
   > 21/2 = 10, remainder is 1
   > 10/2 = 5, remainder is 0
   > 5/2 = 2, remainder is 1
   > 2/2 = 1, remainder is 0
   > 1/2 = 0, remainder is 1
Read remainders from the bottom to top as 10101100
So, 172 of decimal is 10101100 in binary
172 in binary is 10101100

Converting 255 to binary
Divide 255 successively by 2 until the quotient is 0
   > 255/2 = 127, remainder is 1
   > 127/2 = 63, remainder is 1
   > 63/2 = 31, remainder is 1
   > 31/2 = 15, remainder is 1
   > 15/2 = 7, remainder is 1
   > 7/2 = 3, remainder is 1
   > 3/2 = 1, remainder is 1
   > 1/2 = 0, remainder is 1
Read remainders from the bottom to top as 11111111
So, 255 of decimal is 11111111 in binary
255 in binary is 11111111

Converting 14 to binary
Divide 14 successively by 2 until the quotient is 0
   > 14/2 = 7, remainder is 0
   > 7/2 = 3, remainder is 1
   > 3/2 = 1, remainder is 1
   > 1/2 = 0, remainder is 1
Read remainders from the bottom to top as 1110
So, 14 of decimal is 1110 in binary
14 in binary is 00001110

Converting 30 to binary
Divide 30 successively by 2 until the quotient is 0
   > 30/2 = 15, remainder is 0
   > 15/2 = 7, remainder is 1
   > 7/2 = 3, remainder is 1
   > 3/2 = 1, remainder is 1
   > 1/2 = 0, remainder is 1
Read remainders from the bottom to top as 11110
So, 30 of decimal is 11110 in binary
30 in binary is 00011110

====================================================================================
||    172.255.14.30 in binary notation is 10101100.11111111.00001110.00011110    ||
====================================================================================

Subnet mask is /20

For Calculating network ID, keep first 20 bits of 10101100.11111111.00001110.00011110 and set all remaining bits to 0.
so, network ID in binary is 10101100.11111111.00000000.00000000
10101100.11111111.00000000.00000000:
----------------------------------------
10101100.11111111.00000000.00000000
Let's convert all octets to decimal separately
Converting 10101100 to decimal
=> 10101100
=> 1x2^7+0x2^6+1x2^5+0x2^4+1x2^3+1x2^2+0x2^1+0x2^0
=> 1x128+0x64+1x32+0x16+1x8+1x4+0x2+0x1
=> 128+0+32+0+8+4+0+0
=> 172
10101100 in decimal is 172

Converting 11111111 to decimal
=> 11111111
=> 1x2^7+1x2^6+1x2^5+1x2^4+1x2^3+1x2^2+1x2^1+1x2^0
=> 1x128+1x64+1x32+1x16+1x8+1x4+1x2+1x1
=> 128+64+32+16+8+4+2+1
=> 255
11111111 in decimal is 255

Converting 00000000 to decimal
=> 00000000
=> 0x2^7+0x2^6+0x2^5+0x2^4+0x2^3+0x2^2+0x2^1+0x2^0
=> 0x128+0x64+0x32+0x16+0x8+0x4+0x2+0x1
=> 0+0+0+0+0+0+0+0
=> 0
00000000 in decimal is 0

Converting 00000000 to decimal
=> 00000000
=> 0x2^7+0x2^6+0x2^5+0x2^4+0x2^3+0x2^2+0x2^1+0x2^0
=> 0x128+0x64+0x32+0x16+0x8+0x4+0x2+0x1
=> 0+0+0+0+0+0+0+0
=> 0
00000000 in decimal is 0

===================================================================================
||    10101100.11111111.00000000.00000000 in decimal notation is 172.255.0.0    ||
===================================================================================
==========================================
||    So, Network ID is 172.255.0.0    ||
==========================================

Answer:
-------
Network addresses od addresses are 172.255.16.0 and 172.255.0.0 which are different.
so, these devices are not on the same subnet.