Question

On a network with an IP address of 158.234.28.72 and a subnet mask of 255.248.0.0 what is the network ID and the broadcast address? Show your calculations.

Answer 1

158.234.28.72:
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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

255.248.0.0:
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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

0 in binary is 00000000
0 in binary is 00000000

so, 255.248.0.0 in binary notation is 11111111.11111000.00000000.00000000

first 13 bits in subnet mask 255.248.0.0 is 1.
so, for network ID, keep first 13 bits of 158.234.28.72 and set all remaining bits to 0.
so, network ID is 10011110.11101000.00000000.00000000
10011110.11101000.00000000.00000000:
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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

00000000 in decimal is 0
00000000 in decimal is 0

10011110.11101000.00000000.00000000 in binary notation is 158.232.0.0

so, for broadcast ID, keep first 13 bits of 158.234.28.72 and set all remaining bits to 1.
so, broadcast ID is 10011110.11101111.11111111.11111111
10011110.11101111.11111111.11111111:
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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 binary notation is 158.239.255.255


network ID is:  158.232.0.0
broadcast ID is:    158.239.255.255