Question

IP Address: 192.169.69.47

Subnet Mask: 255.255.192.0

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: 192.169.69.47
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Let's first convert this into binary format
192.169.69.47
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 169 to binary
Divide 169 successively by 2 until the quotient is 0
   > 169/2 = 84, remainder is 1
   > 84/2 = 42, remainder is 0
   > 42/2 = 21, remainder is 0
   > 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 10101001
So, 169 of decimal is 10101001 in binary
169 in binary is 10101001

Converting 69 to binary
Divide 69 successively by 2 until the quotient is 0
   > 69/2 = 34, remainder is 1
   > 34/2 = 17, remainder is 0
   > 17/2 = 8, remainder is 1
   > 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 1000101
So, 69 of decimal is 1000101 in binary
69 in binary is 01000101

Converting 47 to binary
Divide 47 successively by 2 until the quotient is 0
   > 47/2 = 23, remainder is 1
   > 23/2 = 11, remainder is 1
   > 11/2 = 5, remainder is 1
   > 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 101111
So, 47 of decimal is 101111 in binary
47 in binary is 00101111

====================================================================================
|| 192.169.69.47 in binary notation is 11000000.10101001.01000101.00101111 ||
====================================================================================

Subnet address: 255.255.192.0
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Let's convert this into binary format
255.255.192.0
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 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 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

====================================================================================
|| 255.255.192.0 in binary notation is 11111111.11111111.11000000.00000000 ||
====================================================================================

Remove all dots to form 11111111111111111100000000000000
Remove all 0's from the right side to form 111111111111111111
Number of 1's in this is 18
so, Subnet mask is /18

For Calculating network ID, keep first 18 bits of 11000000.10101001.01000101.00101111 and set all remaining bits to 0.
so, network ID in binary is 11000000.10101001.01000000.00000000
11000000.10101001.01000000.00000000:
----------------------------------------
11000000.10101001.01000000.00000000
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 10101001 to decimal
=> 10101001
=> 1x2^7+0x2^6+1x2^5+0x2^4+1x2^3+0x2^2+0x2^1+1x2^0
=> 1x128+0x64+1x32+0x16+1x8+0x4+0x2+1x1
=> 128+0+32+0+8+0+0+1
=> 169
10101001 in decimal is 169

Converting 01000000 to decimal
=> 01000000
=> 0x2^7+1x2^6+0x2^5+0x2^4+0x2^3+0x2^2+0x2^1+0x2^0
=> 0x128+1x64+0x32+0x16+0x8+0x4+0x2+0x1
=> 0+64+0+0+0+0+0+0
=> 64
01000000 in decimal is 64

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

====================================================================================
|| 11000000.10101001.01000000.00000000 in decimal notation is 192.169.64.0 ||
====================================================================================
===========================================
|| So, Network ID is 192.169.64.0 ||
===========================================

For Calculating broadcast ID, keep first 18 bits of 11000000.10101001.01000101.00101111 and set all remaining bits to 1.
so, broadcast ID in binary is 11000000.10101001.01111111.11111111
11000000.10101001.01111111.11111111:
----------------------------------------
11000000.10101001.01111111.11111111
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 10101001 to decimal
=> 10101001
=> 1x2^7+0x2^6+1x2^5+0x2^4+1x2^3+0x2^2+0x2^1+1x2^0
=> 1x128+0x64+1x32+0x16+1x8+0x4+0x2+1x1
=> 128+0+32+0+8+0+0+1
=> 169
10101001 in decimal is 169

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

=======================================================================================
|| 11000000.10101001.01111111.11111111 in decimal notation is 192.169.127.255 ||
=======================================================================================
================================================
|| So, broadcast ID is 192.169.127.255 ||
================================================

For Calculating first valid address in subnet, add 1 to the network address.
Network Address is 192.169.64.0
==============================================================
|| So, first valid address in subnet is 192.169.64.1 ||
==============================================================

For Calculating last valid address in subnet, remove 1 from the broadcast address.
Broadcast Address is 192.169.127.255
================================================================
|| So, last valid address in subnet is 192.169.127.254 ||
================================================================

Number of valid hosts in the network
   > 2^(32 - number of 1's in subnet) - 2
   > 2^(32 - 18) - 2
   > 2^(14) - 2
   > 16384 - 2
   > 16382
=============================================================
|| So, number of valid hosts in the subnet is 16382 ||
=============================================================