Question

IP address:  158.234.28.72
Subnet Mask: 255.248.0.0

Find Network Address and Broadcast address. Provide all necessary steps.

Answer 1

IP Address: 158.234.28.72
----------------------------------------
Let's first convert this into binary format
158.234.28.72
Let's convert all octets to binary separately
Converting 158 to binary
Divide 158 successively by 2 until the quotient is 0
158/2 = 79, remainder is 0
79/2 = 39, remainder is 1
39/2 = 19, remainder is 1
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 10011110
158 in binary is 10011110

Converting 234 to binary
Divide 234 successively by 2 until the quotient is 0
234/2 = 117, remainder is 0
117/2 = 58, remainder is 1
58/2 = 29, remainder is 0
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 11101010
234 in binary is 11101010

Converting 28 to binary
Divide 28 successively by 2 until the quotient 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 11100
28 in binary is 00011100

Converting 72 to binary
Divide 72 successively by 2 until the quotient 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 1001000
72 in binary is 01001000

====================================================================================
||    158.234.28.72 in binary notation is 10011110.11101010.00011100.01001000    ||
====================================================================================

Subnet address: 255.248.0.0
----------------------------------------
Let's convert this into binary format
255.248.0.0
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
255 in binary is 11111111

Converting 248 to binary
Divide 248 successively by 2 until the quotient is 0
248/2 = 124, remainder is 0
124/2 = 62, remainder is 0
62/2 = 31, remainder is 0
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 11111000
248 in binary is 11111000

Converting 0 to binary
Divide 0 successively by 2 until the quotient is 0
Read remainders from the bottom to top as 
0 in binary is 00000000

Converting 0 to binary
Divide 0 successively by 2 until the quotient is 0
Read remainders from the bottom to top as 
0 in binary is 00000000

==================================================================================
||    255.248.0.0 in binary notation is 11111111.11111000.00000000.00000000    ||
==================================================================================

Remove all dots to form 11111111111110000000000000000000
Remove all 0's from the right side to form 1111111111111
Number of 1's in this is 13
so, Subnet mask is /13

For Calculating network ID, keep first 13 bits of 10011110.11101010.00011100.01001000 and set all remaining bits to 0.
so, network ID in binary is 10011110.11101000.00000000.00000000
10011110.11101000.00000000.00000000:
----------------------------------------
10011110.11101000.00000000.00000000
Let's convert all octets to decimal separately
Converting 10011110 to decimal
=> 10011110
=> 1x2^7+0x2^6+0x2^5+1x2^4+1x2^3+1x2^2+1x2^1+0x2^0
=> 1x128+0x64+0x32+1x16+1x8+1x4+1x2+0x1
=> 128+0+0+16+8+4+2+0
=> 158
10011110 in decimal is 158

Converting 11101000 to decimal
=> 11101000
=> 1x2^7+1x2^6+1x2^5+0x2^4+1x2^3+0x2^2+0x2^1+0x2^0
=> 1x128+1x64+1x32+0x16+1x8+0x4+0x2+0x1
=> 128+64+32+0+8+0+0+0
=> 232
11101000 in decimal is 232

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

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

===================================================================================
||    10011110.11101000.00000000.00000000 in decimal notation is 158.232.0.0    ||
===================================================================================
==========================================
||    So, Network ID is 158.232.0.0    ||
==========================================

For Calculating broadcast ID, keep first 13 bits of 10011110.11101010.00011100.01001000 and set all remaining bits to 1.
so, broadcast ID in binary is 10011110.11101111.11111111.11111111
10011110.11101111.11111111.11111111:
----------------------------------------
10011110.11101111.11111111.11111111
Let's convert all octets to decimal separately
Converting 10011110 to decimal
=> 10011110
=> 1x2^7+0x2^6+0x2^5+1x2^4+1x2^3+1x2^2+1x2^1+0x2^0
=> 1x128+0x64+0x32+1x16+1x8+1x4+1x2+0x1
=> 128+0+0+16+8+4+2+0
=> 158
10011110 in decimal is 158

Converting 11101111 to decimal
=> 11101111
=> 1x2^7+1x2^6+1x2^5+0x2^4+1x2^3+1x2^2+1x2^1+1x2^0
=> 1x128+1x64+1x32+0x16+1x8+1x4+1x2+1x1
=> 128+64+32+0+8+4+2+1
=> 239
11101111 in decimal is 239

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
=> 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

=======================================================================================
||    10011110.11101111.11111111.11111111 in decimal notation is 158.239.255.255    ||
=======================================================================================
================================================
||    So, broadcast ID is 158.239.255.255    ||
================================================