Question

Enter the last usable host on the network of which the host 74.200.198.88/27 is a part.

Answer 1

74.200.198.94

Explanation:
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IP Address: 74.200.198.88
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Let's first convert this into binary format
74.200.198.88
Let's convert all octets to binary separately
Converting 74 to binary
Divide 74 successively by 2 until the quotient is 0
   > 74/2 = 37, remainder 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 1001010
So, 74 of decimal is 1001010 in binary
74 in binary is 01001010

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

Converting 198 to binary
Divide 198 successively by 2 until the quotient is 0
   > 198/2 = 99, remainder 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 11000110
So, 198 of decimal is 11000110 in binary
198 in binary is 11000110

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

====================================================================================
||    74.200.198.88 in binary notation is 01001010.11001000.11000110.01011000    ||
====================================================================================

Subnet mask is /27

For Calculating broadcast ID, keep first 27 bits of 01001010.11001000.11000110.01011000 and set all remaining bits to 1.
so, broadcast ID in binary is 01001010.11001000.11000110.01011111
01001010.11001000.11000110.01011111:
----------------------------------------
01001010.11001000.11000110.01011111
Let's convert all octets to decimal separately
Converting 01001010 to decimal
Converting 01001010 to decimal
01001010
=> 0x2^7+1x2^6+0x2^5+0x2^4+1x2^3+0x2^2+1x2^1+0x2^0
=> 0x128+1x64+0x32+0x16+1x8+0x4+1x2+0x1
=> 0+64+0+0+8+0+2+0
=> 74
01001010 in decimal is 74

Converting 11001000 to decimal
Converting 11001000 to decimal
11001000
=> 1x2^7+1x2^6+0x2^5+0x2^4+1x2^3+0x2^2+0x2^1+0x2^0
=> 1x128+1x64+0x32+0x16+1x8+0x4+0x2+0x1
=> 128+64+0+0+8+0+0+0
=> 200
11001000 in decimal is 200

Converting 11000110 to decimal
Converting 11000110 to decimal
11000110
=> 1x2^7+1x2^6+0x2^5+0x2^4+0x2^3+1x2^2+1x2^1+0x2^0
=> 1x128+1x64+0x32+0x16+0x8+1x4+1x2+0x1
=> 128+64+0+0+0+4+2+0
=> 198
11000110 in decimal is 198

Converting 01011111 to decimal
Converting 01011111 to decimal
01011111
=> 0x2^7+1x2^6+0x2^5+1x2^4+1x2^3+1x2^2+1x2^1+1x2^0
=> 0x128+1x64+0x32+1x16+1x8+1x4+1x2+1x1
=> 0+64+0+16+8+4+2+1
=> 95
01011111 in decimal is 95

=====================================================================================
||    01001010.11001000.11000110.01011111 in decimal notation is 74.200.198.95    ||
=====================================================================================
==============================================
||    So, broadcast ID is 74.200.198.95    ||
==============================================

For Calculating last valid address in subnet, remove 1 from the broadcast address.
Broadcast Address is 74.200.198.95
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||    So, last valid address in subnet is 74.200.198.94    ||
==============================================================