Question

Enter the network address of the subnet to which the host 222.242.88.128/28 belongs.

Please show work.

Answer 1

222.242.88.128

Explanation:
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IP Address: 222.242.88.128
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Let's first convert this into binary format
222.242.88.128
Let's convert all octets to binary separately
Converting 222 to binary
Divide 222 successively by 2 until the quotient is 0
   > 222/2 = 111, remainder is 0
   > 111/2 = 55, remainder is 1
   > 55/2 = 27, remainder is 1
   > 27/2 = 13, remainder is 1
   > 13/2 = 6, remainder is 1
   > 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 11011110
So, 222 of decimal is 11011110 in binary
222 in binary is 11011110

Converting 242 to binary
Divide 242 successively by 2 until the quotient is 0
   > 242/2 = 121, remainder is 0
   > 121/2 = 60, remainder is 1
   > 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 11110010
So, 242 of decimal is 11110010 in binary
242 in binary is 11110010

Converting 88 to binary
Divide 88 successively by 2 until the quotient is 0
   > 88/2 = 44, remainder is 0
   > 44/2 = 22, remainder is 0
   > 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 1011000
So, 88 of decimal is 1011000 in binary
88 in binary is 01011000

Converting 128 to binary
Divide 128 successively by 2 until the quotient is 0
   > 128/2 = 64, remainder is 0
   > 64/2 = 32, remainder is 0
   > 32/2 = 16, remainder is 0
   > 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 10000000
So, 128 of decimal is 10000000 in binary
128 in binary is 10000000

=====================================================================================
||    222.242.88.128 in binary notation is 11011110.11110010.01011000.10000000    ||
=====================================================================================

Subnet mask is /28

For Calculating network ID, keep first 28 bits of 11011110.11110010.01011000.10000000 and set all remaining bits to 0.
so, network ID in binary is 11011110.11110010.01011000.10000000
11011110.11110010.01011000.10000000:
----------------------------------------
11011110.11110010.01011000.10000000
Let's convert all octets to decimal separately
Converting 11011110 to decimal
Converting 11011110 to decimal
11011110
=> 1x2^7+1x2^6+0x2^5+1x2^4+1x2^3+1x2^2+1x2^1+0x2^0
=> 1x128+1x64+0x32+1x16+1x8+1x4+1x2+0x1
=> 128+64+0+16+8+4+2+0
=> 222
11011110 in decimal is 222

Converting 11110010 to decimal
Converting 11110010 to decimal
11110010
=> 1x2^7+1x2^6+1x2^5+1x2^4+0x2^3+0x2^2+1x2^1+0x2^0
=> 1x128+1x64+1x32+1x16+0x8+0x4+1x2+0x1
=> 128+64+32+16+0+0+2+0
=> 242
11110010 in decimal is 242

Converting 01011000 to decimal
Converting 01011000 to decimal
01011000
=> 0x2^7+1x2^6+0x2^5+1x2^4+1x2^3+0x2^2+0x2^1+0x2^0
=> 0x128+1x64+0x32+1x16+1x8+0x4+0x2+0x1
=> 0+64+0+16+8+0+0+0
=> 88
01011000 in decimal is 88

Converting 10000000 to decimal
Converting 10000000 to decimal
10000000
=> 1x2^7+0x2^6+0x2^5+0x2^4+0x2^3+0x2^2+0x2^1+0x2^0
=> 1x128+0x64+0x32+0x16+0x8+0x4+0x2+0x1
=> 128+0+0+0+0+0+0+0
=> 128
10000000 in decimal is 128

======================================================================================
||    11011110.11110010.01011000.10000000 in decimal notation is 222.242.88.128    ||
======================================================================================
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||    So, Network ID is 222.242.88.128    ||
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