Question

Enter the usable host range for the network of which the IP address 11.77.132.239 255.255.255.224 is a part.

Please show work.

Answer 1

11.77.132.225 to 11.77.132.254

Explanation:
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IP Address: 11.77.132.239
----------------------------------------
Let's first convert this into binary format
11.77.132.239
Let's convert all octets to binary separately
Converting 11 to binary
Divide 11 successively by 2 until the quotient 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 1011
So, 11 of decimal is 1011 in binary
11 in binary is 00001011

Converting 77 to binary
Divide 77 successively by 2 until the quotient is 0
   > 77/2 = 38, remainder is 1
   > 38/2 = 19, remainder is 0
   > 19/2 = 9, remainder is 1
   > 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 1001101
So, 77 of decimal is 1001101 in binary
77 in binary is 01001101

Converting 132 to binary
Divide 132 successively by 2 until the quotient is 0
   > 132/2 = 66, remainder is 0
   > 66/2 = 33, remainder is 0
   > 33/2 = 16, remainder is 1
   > 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 10000100
So, 132 of decimal is 10000100 in binary
132 in binary is 10000100

Converting 239 to binary
Divide 239 successively by 2 until the quotient is 0
   > 239/2 = 119, remainder is 1
   > 119/2 = 59, remainder is 1
   > 59/2 = 29, remainder is 1
   > 29/2 = 14, remainder is 1
   > 14/2 = 7, remainder is 0
   > 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 11101111
So, 239 of decimal is 11101111 in binary
239 in binary is 11101111

====================================================================================
||    11.77.132.239 in binary notation is 00001011.01001101.10000100.11101111    ||
====================================================================================

Subnet address: 255.255.255.224
----------------------------------------
Let's convert this into binary format
255.255.255.224
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 224 to binary
Divide 224 successively by 2 until the quotient is 0
   > 224/2 = 112, remainder is 0
   > 112/2 = 56, remainder is 0
   > 56/2 = 28, remainder is 0
   > 28/2 = 14, remainder is 0
   > 14/2 = 7, remainder is 0
   > 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 11100000
So, 224 of decimal is 11100000 in binary
224 in binary is 11100000

======================================================================================
||    255.255.255.224 in binary notation is 11111111.11111111.11111111.11100000    ||
======================================================================================

Remove all dots to form 11111111111111111111111111100000
Remove all 0's from the right side to form 111111111111111111111111111
Number of 1's in this is 27
so, Subnet mask is /27

For Calculating network ID, keep first 27 bits of 00001011.01001101.10000100.11101111 and set all remaining bits to 0.
so, network ID in binary is 00001011.01001101.10000100.11100000
00001011.01001101.10000100.11100000:
----------------------------------------
00001011.01001101.10000100.11100000
Let's convert all octets to decimal separately
Converting 00001011 to decimal
Converting 00001011 to decimal
00001011
=> 0x2^7+0x2^6+0x2^5+0x2^4+1x2^3+0x2^2+1x2^1+1x2^0
=> 0x128+0x64+0x32+0x16+1x8+0x4+1x2+1x1
=> 0+0+0+0+8+0+2+1
=> 11
00001011 in decimal is 11

Converting 01001101 to decimal
Converting 01001101 to decimal
01001101
=> 0x2^7+1x2^6+0x2^5+0x2^4+1x2^3+1x2^2+0x2^1+1x2^0
=> 0x128+1x64+0x32+0x16+1x8+1x4+0x2+1x1
=> 0+64+0+0+8+4+0+1
=> 77
01001101 in decimal is 77

Converting 10000100 to decimal
Converting 10000100 to decimal
10000100
=> 1x2^7+0x2^6+0x2^5+0x2^4+0x2^3+1x2^2+0x2^1+0x2^0
=> 1x128+0x64+0x32+0x16+0x8+1x4+0x2+0x1
=> 128+0+0+0+0+4+0+0
=> 132
10000100 in decimal is 132

Converting 11100000 to decimal
Converting 11100000 to decimal
11100000
=> 1x2^7+1x2^6+1x2^5+0x2^4+0x2^3+0x2^2+0x2^1+0x2^0
=> 1x128+1x64+1x32+0x16+0x8+0x4+0x2+0x1
=> 128+64+32+0+0+0+0+0
=> 224
11100000 in decimal is 224

=====================================================================================
||    00001011.01001101.10000100.11100000 in decimal notation is 11.77.132.224    ||
=====================================================================================
============================================
||    So, Network ID is 11.77.132.224    ||
============================================

For Calculating broadcast ID, keep first 27 bits of 00001011.01001101.10000100.11101111 and set all remaining bits to 1.
so, broadcast ID in binary is 00001011.01001101.10000100.11111111
00001011.01001101.10000100.11111111:
----------------------------------------
00001011.01001101.10000100.11111111
Let's convert all octets to decimal separately
Converting 00001011 to decimal
Converting 00001011 to decimal
00001011
=> 0x2^7+0x2^6+0x2^5+0x2^4+1x2^3+0x2^2+1x2^1+1x2^0
=> 0x128+0x64+0x32+0x16+1x8+0x4+1x2+1x1
=> 0+0+0+0+8+0+2+1
=> 11
00001011 in decimal is 11

Converting 01001101 to decimal
Converting 01001101 to decimal
01001101
=> 0x2^7+1x2^6+0x2^5+0x2^4+1x2^3+1x2^2+0x2^1+1x2^0
=> 0x128+1x64+0x32+0x16+1x8+1x4+0x2+1x1
=> 0+64+0+0+8+4+0+1
=> 77
01001101 in decimal is 77

Converting 10000100 to decimal
Converting 10000100 to decimal
10000100
=> 1x2^7+0x2^6+0x2^5+0x2^4+0x2^3+1x2^2+0x2^1+0x2^0
=> 1x128+0x64+0x32+0x16+0x8+1x4+0x2+0x1
=> 128+0+0+0+0+4+0+0
=> 132
10000100 in decimal is 132

Converting 11111111 to decimal
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

=====================================================================================
||    00001011.01001101.10000100.11111111 in decimal notation is 11.77.132.255    ||
=====================================================================================
==============================================
||    So, broadcast ID is 11.77.132.255    ||
==============================================

For Calculating first valid address in subnet, add 1 to the network address.
Network Address is 11.77.132.224
===============================================================
||    So, first valid address in subnet is 11.77.132.225    ||
===============================================================

For Calculating last valid address in subnet, remove 1 from the broadcast address.
Broadcast Address is 11.77.132.255
==============================================================
||    So, last valid address in subnet is 11.77.132.254    ||
==============================================================