Question

calculate the network portion address where the host resides under the assumption of Host IP address = 10.0.1.130 and subnet mask = 255.255.255.128

Answer 1

Answer:
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10.0.1.128

Explanation:
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IP Address: 10.0.1.130
----------------------------------------
Let's first convert this into binary format
10.0.1.130
Let's convert all octets to binary separately
Converting 10 to binary
Divide 10 successively by 2 until the quotient is 0
   > 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 1010
So, 10 of decimal is 1010 in binary
10 in binary is 00001010

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

Converting 1 to binary
Divide 1 successively by 2 until the quotient is 0
   > 1/2 = 0, remainder is 1
Read remainders from the bottom to top as 1
So, 1 of decimal is 1 in binary
1 in binary is 00000001

Converting 130 to binary
Divide 130 successively by 2 until the quotient is 0
   > 130/2 = 65, remainder is 0
   > 65/2 = 32, remainder is 1
   > 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 10000010
So, 130 of decimal is 10000010 in binary
130 in binary is 10000010

=================================================================================
||    10.0.1.130 in binary notation is 00001010.00000000.00000001.10000010    ||
=================================================================================

Subnet address: 255.255.255.128
----------------------------------------
Let's convert this into binary format
255.255.255.128
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 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 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 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

======================================================================================
||    255.255.255.128 in binary notation is 11111111.11111111.11111111.10000000    ||
======================================================================================

Remove all dots to form 11111111111111111111111110000000
Remove all 0's from the right side to form 1111111111111111111111111
Number of 1's in this is 25
so, Subnet mask is /25

For Calculating network ID, keep first 25 bits of 00001010.00000000.00000001.10000010 and set all remaining bits to 0.
so, network ID in binary is 00001010.00000000.00000001.10000000
00001010.00000000.00000001.10000000:
----------------------------------------
00001010.00000000.00000001.10000000
Let's convert all octets to decimal separately
Converting 00001010 to decimal
Converting 00001010 to decimal
00001010
=> 0x2^7+0x2^6+0x2^5+0x2^4+1x2^3+0x2^2+1x2^1+0x2^0
=> 0x128+0x64+0x32+0x16+1x8+0x4+1x2+0x1
=> 0+0+0+0+8+0+2+0
=> 10
00001010 in decimal is 10

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

Converting 00000001 to decimal
Converting 00000001 to decimal
00000001
=> 0x2^7+0x2^6+0x2^5+0x2^4+0x2^3+0x2^2+0x2^1+1x2^0
=> 0x128+0x64+0x32+0x16+0x8+0x4+0x2+1x1
=> 0+0+0+0+0+0+0+1
=> 1
00000001 in decimal is 1

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

==================================================================================
||    00001010.00000000.00000001.10000000 in decimal notation is 10.0.1.128    ||
==================================================================================
=========================================
||    So, Network ID is 10.0.1.128    ||
=========================================