Question

IP Address: 37.124.67.99

Subnet Mask: 255.240.0.0

find Network address, Broadcast address, first valid host address, last valid host address and number of valid hosts in the network.

show very clear steps for all the calculations.

Answer 1

IP Address: 37.124.67.99
----------------------------------------
Let's first convert this into binary format
37.124.67.99
Let's convert all octets to binary separately
Converting 37 to binary
Divide 37 successively by 2 until the quotient is 0
   > 37/2 = 18, remainder is 1
   > 18/2 = 9, remainder is 0
   > 9/2 = 4, remainder is 1
   > 4/2 = 2, remainder is 0
   > 2/2 = 1, remainder is 0
   > 1/2 = 0, remainder is 1
Read remainders from the bottom to top as 100101
So, 37 of decimal is 100101 in binary
37 in binary is 00100101

Converting 124 to binary
Divide 124 successively by 2 until the quotient is 0
   > 124/2 = 62, remainder is 0
   > 62/2 = 31, remainder is 0
   > 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 1111100
So, 124 of decimal is 1111100 in binary
124 in binary is 01111100

Converting 67 to binary
Divide 67 successively by 2 until the quotient is 0
   > 67/2 = 33, remainder is 1
   > 33/2 = 16, remainder is 1
   > 16/2 = 8, remainder is 0
   > 8/2 = 4, remainder is 0
   > 4/2 = 2, remainder is 0
   > 2/2 = 1, remainder is 0
   > 1/2 = 0, remainder is 1
Read remainders from the bottom to top as 1000011
So, 67 of decimal is 1000011 in binary
67 in binary is 01000011

Converting 99 to binary
Divide 99 successively by 2 until the quotient is 0
   > 99/2 = 49, remainder is 1
   > 49/2 = 24, remainder is 1
   > 24/2 = 12, remainder is 0
   > 12/2 = 6, remainder is 0
   > 6/2 = 3, remainder is 0
   > 3/2 = 1, remainder is 1
   > 1/2 = 0, remainder is 1
Read remainders from the bottom to top as 1100011
So, 99 of decimal is 1100011 in binary
99 in binary is 01100011

===================================================================================
|| 37.124.67.99 in binary notation is 00100101.01111100.01000011.01100011 ||
===================================================================================

Subnet address: 255.240.0.0
----------------------------------------
Let's convert this into binary format
255.240.0.0
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 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

Converting 0 to binary
Divide 0 successively by 2 until the quotient is 0
Read remainders from the bottom to top as
So, 0 of decimal is in binary
0 in binary is 00000000

Converting 0 to binary
Divide 0 successively by 2 until the quotient is 0
Read remainders from the bottom to top as
So, 0 of decimal is in binary
0 in binary is 00000000

==================================================================================
|| 255.240.0.0 in binary notation is 11111111.11110000.00000000.00000000 ||
==================================================================================

Remove all dots to form 11111111111100000000000000000000
Remove all 0's from the right side to form 111111111111
Number of 1's in this is 12
so, Subnet mask is /12

For Calculating network ID, keep first 12 bits of 00100101.01111100.01000011.01100011 and set all remaining bits to 0.
so, network ID in binary is 00100101.01110000.00000000.00000000
00100101.01110000.00000000.00000000:
----------------------------------------
00100101.01110000.00000000.00000000
Let's convert all octets to decimal separately
Converting 00100101 to decimal
=> 00100101
=> 0x2^7+0x2^6+1x2^5+0x2^4+0x2^3+1x2^2+0x2^1+1x2^0
=> 0x128+0x64+1x32+0x16+0x8+1x4+0x2+1x1
=> 0+0+32+0+0+4+0+1
=> 37
00100101 in decimal is 37

Converting 01110000 to decimal
=> 01110000
=> 0x2^7+1x2^6+1x2^5+1x2^4+0x2^3+0x2^2+0x2^1+0x2^0
=> 0x128+1x64+1x32+1x16+0x8+0x4+0x2+0x1
=> 0+64+32+16+0+0+0+0
=> 112
01110000 in decimal is 112

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

==================================================================================
|| 00100101.01110000.00000000.00000000 in decimal notation is 37.112.0.0 ||
==================================================================================
=========================================
|| So, Network ID is 37.112.0.0 ||
=========================================

For Calculating broadcast ID, keep first 12 bits of 00100101.01111100.01000011.01100011 and set all remaining bits to 1.
so, broadcast ID in binary is 00100101.01111111.11111111.11111111
00100101.01111111.11111111.11111111:
----------------------------------------
00100101.01111111.11111111.11111111
Let's convert all octets to decimal separately
Converting 00100101 to decimal
=> 00100101
=> 0x2^7+0x2^6+1x2^5+0x2^4+0x2^3+1x2^2+0x2^1+1x2^0
=> 0x128+0x64+1x32+0x16+0x8+1x4+0x2+1x1
=> 0+0+32+0+0+4+0+1
=> 37
00100101 in decimal is 37

Converting 01111111 to decimal
=> 01111111
=> 0x2^7+1x2^6+1x2^5+1x2^4+1x2^3+1x2^2+1x2^1+1x2^0
=> 0x128+1x64+1x32+1x16+1x8+1x4+1x2+1x1
=> 0+64+32+16+8+4+2+1
=> 127
01111111 in decimal is 127

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 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

======================================================================================
|| 00100101.01111111.11111111.11111111 in decimal notation is 37.127.255.255 ||
======================================================================================
===============================================
|| So, broadcast ID is 37.127.255.255 ||
===============================================

For Calculating first valid address in subnet, add 1 to the network address.
Network Address is 37.112.0.0
============================================================
|| So, first valid address in subnet is 37.112.0.1 ||
============================================================

For Calculating last valid address in subnet, remove 1 from the broadcast address.
Broadcast Address is 37.127.255.255
===============================================================
|| So, last valid address in subnet is 37.127.255.254 ||
===============================================================

Number of valid hosts in the network
   > 2^(32 - number of 1's in subnet) - 2
   > 2^(32 - 12) - 2
   > 2^(20) - 2
   > 1048576 - 2
   > 1048574
===============================================================
|| So, number of valid hosts in the subnet is 1048574 ||
===============================================================