Question

Enter the first usable host address on the network 181.15.144.200 255.255.255.192.

Please show work.

Answer 1

181.15.144.193

Explanation:
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IP Address: 181.15.144.200
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Let's first convert this into binary format
181.15.144.200
Let's convert all octets to binary separately
Converting 181 to binary
Divide 181 successively by 2 until the quotient is 0
   > 181/2 = 90, remainder is 1
   > 90/2 = 45, remainder is 0
   > 45/2 = 22, remainder is 1
   > 22/2 = 11, remainder is 0
   > 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 10110101
So, 181 of decimal is 10110101 in binary
181 in binary is 10110101

Converting 15 to binary
Divide 15 successively by 2 until the quotient 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 1111
So, 15 of decimal is 1111 in binary
15 in binary is 00001111

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 200 to binary
Divide 200 successively by 2 until the quotient is 0
   > 200/2 = 100, remainder is 0
   > 100/2 = 50, remainder is 0
   > 50/2 = 25, remainder is 0
   > 25/2 = 12, remainder is 1
   > 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 11001000
So, 200 of decimal is 11001000 in binary
200 in binary is 11001000

=====================================================================================
||    181.15.144.200 in binary notation is 10110101.00001111.10010000.11001000    ||
=====================================================================================

Subnet address: 255.255.255.192
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Let's convert this into binary format
255.255.255.192
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 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

======================================================================================
||    255.255.255.192 in binary notation is 11111111.11111111.11111111.11000000    ||
======================================================================================

Remove all dots to form 11111111111111111111111111000000
Remove all 0's from the right side to form 11111111111111111111111111
Number of 1's in this is 26
so, Subnet mask is /26

For Calculating network ID, keep first 26 bits of 10110101.00001111.10010000.11001000 and set all remaining bits to 0.
so, network ID in binary is 10110101.00001111.10010000.11000000
10110101.00001111.10010000.11000000:
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10110101.00001111.10010000.11000000
Let's convert all octets to decimal separately
Converting 10110101 to decimal
Converting 10110101 to decimal
10110101
=> 1x2^7+0x2^6+1x2^5+1x2^4+0x2^3+1x2^2+0x2^1+1x2^0
=> 1x128+0x64+1x32+1x16+0x8+1x4+0x2+1x1
=> 128+0+32+16+0+4+0+1
=> 181
10110101 in decimal is 181

Converting 00001111 to decimal
Converting 00001111 to decimal
00001111
=> 0x2^7+0x2^6+0x2^5+0x2^4+1x2^3+1x2^2+1x2^1+1x2^0
=> 0x128+0x64+0x32+0x16+1x8+1x4+1x2+1x1
=> 0+0+0+0+8+4+2+1
=> 15
00001111 in decimal is 15

Converting 10010000 to decimal
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 11000000 to decimal
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

======================================================================================
||    10110101.00001111.10010000.11000000 in decimal notation is 181.15.144.192    ||
======================================================================================
=============================================
||    So, Network ID is 181.15.144.192    ||
=============================================

For Calculating first valid address in subnet, add 1 to the network address.
Network Address is 181.15.144.192
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||    So, first valid address in subnet is 181.15.144.193    ||
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