Question

Find the network address, the direct broadcast address, and the number of addresses in a block; if one of the addresses in this block is 175.120.240.17/19

Answer 1

Network address is 175.120.224.0
broadcast address is 175.120.255.255
number of addresses in a block is 2^(32-19) = 2^13 = 8192

Explanation:
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IP Address: 175.120.240.17
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Let's first convert this into binary format
175.120.240.17
Let's convert all octets to binary separately
Converting 175 to binary
Divide 175 successively by 2 until the quotient is 0
   > 175/2 = 87, remainder is 1
   > 87/2 = 43, remainder is 1
   > 43/2 = 21, remainder is 1
   > 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 10101111
So, 175 of decimal is 10101111 in binary
175 in binary is 10101111

Converting 120 to binary
Divide 120 successively by 2 until the quotient is 0
   > 120/2 = 60, remainder is 0
   > 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 1111000
So, 120 of decimal is 1111000 in binary
120 in binary is 01111000

Converting 240 to binary
Divide 240 successively by 2 until the quotient is 0
   > 240/2 = 120, remainder is 0
   > 120/2 = 60, remainder is 0
   > 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 11110000
So, 240 of decimal is 11110000 in binary
240 in binary is 11110000

Converting 17 to binary
Divide 17 successively by 2 until the quotient 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 10001
So, 17 of decimal is 10001 in binary
17 in binary is 00010001

=====================================================================================
||    175.120.240.17 in binary notation is 10101111.01111000.11110000.00010001    ||
=====================================================================================

Subnet mask is /19

For Calculating network ID, keep first 19 bits of 10101111.01111000.11110000.00010001 and set all remaining bits to 0.
so, network ID in binary is 10101111.01111000.11100000.00000000
10101111.01111000.11100000.00000000:
----------------------------------------
10101111.01111000.11100000.00000000
Let's convert all octets to decimal separately
Converting 10101111 to decimal
Converting 10101111 to decimal
10101111
=> 1x2^7+0x2^6+1x2^5+0x2^4+1x2^3+1x2^2+1x2^1+1x2^0
=> 1x128+0x64+1x32+0x16+1x8+1x4+1x2+1x1
=> 128+0+32+0+8+4+2+1
=> 175
10101111 in decimal is 175

Converting 01111000 to decimal
Converting 01111000 to decimal
01111000
=> 0x2^7+1x2^6+1x2^5+1x2^4+1x2^3+0x2^2+0x2^1+0x2^0
=> 0x128+1x64+1x32+1x16+1x8+0x4+0x2+0x1
=> 0+64+32+16+8+0+0+0
=> 120
01111000 in decimal is 120

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

Converting 00000000 to decimal
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

=====================================================================================
||    10101111.01111000.11100000.00000000 in decimal notation is 175.120.224.0    ||
=====================================================================================
============================================
||    So, Network ID is 175.120.224.0    ||
============================================

For Calculating broadcast ID, keep first 19 bits of 10101111.01111000.11110000.00010001 and set all remaining bits to 1.
so, broadcast ID in binary is 10101111.01111000.11111111.11111111
10101111.01111000.11111111.11111111:
----------------------------------------
10101111.01111000.11111111.11111111
Let's convert all octets to decimal separately
Converting 10101111 to decimal
Converting 10101111 to decimal
10101111
=> 1x2^7+0x2^6+1x2^5+0x2^4+1x2^3+1x2^2+1x2^1+1x2^0
=> 1x128+0x64+1x32+0x16+1x8+1x4+1x2+1x1
=> 128+0+32+0+8+4+2+1
=> 175
10101111 in decimal is 175

Converting 01111000 to decimal
Converting 01111000 to decimal
01111000
=> 0x2^7+1x2^6+1x2^5+1x2^4+1x2^3+0x2^2+0x2^1+0x2^0
=> 0x128+1x64+1x32+1x16+1x8+0x4+0x2+0x1
=> 0+64+32+16+8+0+0+0
=> 120
01111000 in decimal is 120

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

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

=======================================================================================
||    10101111.01111000.11111111.11111111 in decimal notation is 175.120.255.255    ||
=======================================================================================
================================================
||    So, broadcast ID is 175.120.255.255    ||
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