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IP Address: 192.144.96.0

Subnet Mask: 255.255.240.0

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: 192.144.96.0
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Let's first convert this into binary format
192.144.96.0
Let's convert all octets to binary separately
Converting 192 to binary
Divide 192 successively by 2 until the quotient is 0
   > 192/2 = 96, remainder is 0
   > 96/2 = 48, remainder is 0
   > 48/2 = 24, remainder is 0
   > 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 11000000
So, 192 of decimal is 11000000 in binary
192 in binary is 11000000

Converting 144 to binary
Divide 144 successively by 2 until the quotient is 0
   > 144/2 = 72, remainder is 0
   > 72/2 = 36, remainder is 0
   > 36/2 = 18, remainder is 0
   > 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 10010000
So, 144 of decimal is 10010000 in binary
144 in binary is 10010000

Converting 96 to binary
Divide 96 successively by 2 until the quotient is 0
   > 96/2 = 48, remainder is 0
   > 48/2 = 24, remainder is 0
   > 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 1100000
So, 96 of decimal is 1100000 in binary
96 in binary is 01100000

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

===================================================================================
|| 192.144.96.0 in binary notation is 11000000.10010000.01100000.00000000 ||
===================================================================================

Subnet address: 255.255.240.0
----------------------------------------
Let's convert this into binary format
255.255.240.0
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 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

====================================================================================
|| 255.255.240.0 in binary notation is 11111111.11111111.11110000.00000000 ||
====================================================================================

Remove all dots to form 11111111111111111111000000000000
Remove all 0's from the right side to form 11111111111111111111
Number of 1's in this is 20
so, Subnet mask is /20

For Calculating network ID, keep first 20 bits of 11000000.10010000.01100000.00000000 and set all remaining bits to 0.
so, network ID in binary is 11000000.10010000.01100000.00000000
11000000.10010000.01100000.00000000:
----------------------------------------
11000000.10010000.01100000.00000000
Let's convert all octets to decimal separately
Converting 11000000 to decimal
=> 11000000
=> 1x2^7+1x2^6+0x2^5+0x2^4+0x2^3+0x2^2+0x2^1+0x2^0
=> 1x128+1x64+0x32+0x16+0x8+0x4+0x2+0x1
=> 128+64+0+0+0+0+0+0
=> 192
11000000 in decimal is 192

Converting 10010000 to decimal
=> 10010000
=> 1x2^7+0x2^6+0x2^5+1x2^4+0x2^3+0x2^2+0x2^1+0x2^0
=> 1x128+0x64+0x32+1x16+0x8+0x4+0x2+0x1
=> 128+0+0+16+0+0+0+0
=> 144
10010000 in decimal is 144

Converting 01100000 to decimal
=> 01100000
=> 0x2^7+1x2^6+1x2^5+0x2^4+0x2^3+0x2^2+0x2^1+0x2^0
=> 0x128+1x64+1x32+0x16+0x8+0x4+0x2+0x1
=> 0+64+32+0+0+0+0+0
=> 96
01100000 in decimal is 96

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

====================================================================================
|| 11000000.10010000.01100000.00000000 in decimal notation is 192.144.96.0 ||
====================================================================================
===========================================
|| So, Network ID is 192.144.96.0 ||
===========================================

For Calculating broadcast ID, keep first 20 bits of 11000000.10010000.01100000.00000000 and set all remaining bits to 1.
so, broadcast ID in binary is 11000000.10010000.01101111.11111111
11000000.10010000.01101111.11111111:
----------------------------------------
11000000.10010000.01101111.11111111
Let's convert all octets to decimal separately
Converting 11000000 to decimal
=> 11000000
=> 1x2^7+1x2^6+0x2^5+0x2^4+0x2^3+0x2^2+0x2^1+0x2^0
=> 1x128+1x64+0x32+0x16+0x8+0x4+0x2+0x1
=> 128+64+0+0+0+0+0+0
=> 192
11000000 in decimal is 192

Converting 10010000 to decimal
=> 10010000
=> 1x2^7+0x2^6+0x2^5+1x2^4+0x2^3+0x2^2+0x2^1+0x2^0
=> 1x128+0x64+0x32+1x16+0x8+0x4+0x2+0x1
=> 128+0+0+16+0+0+0+0
=> 144
10010000 in decimal is 144

Converting 01101111 to decimal
=> 01101111
=> 0x2^7+1x2^6+1x2^5+0x2^4+1x2^3+1x2^2+1x2^1+1x2^0
=> 0x128+1x64+1x32+0x16+1x8+1x4+1x2+1x1
=> 0+64+32+0+8+4+2+1
=> 111
01101111 in decimal is 111

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

=======================================================================================
|| 11000000.10010000.01101111.11111111 in decimal notation is 192.144.111.255 ||
=======================================================================================
================================================
|| So, broadcast ID is 192.144.111.255 ||
================================================

For Calculating first valid address in subnet, add 1 to the network address.
Network Address is 192.144.96.0
==============================================================
|| So, first valid address in subnet is 192.144.96.1 ||
==============================================================

For Calculating last valid address in subnet, remove 1 from the broadcast address.
Broadcast Address is 192.144.111.255
================================================================
|| So, last valid address in subnet is 192.144.111.254 ||
================================================================

Number of valid hosts in the network
   > 2^(32 - number of 1's in subnet) - 2
   > 2^(32 - 20) - 2
   > 2^(12) - 2
   > 4096 - 2
   > 4094
============================================================
|| So, number of valid hosts in the subnet is 4094 ||
============================================================