Chapter 1 | Routing TCP/IP, Volume 1 (2nd Edition)

If the first four bits of a class D address are 1110, the lowest first octet is 11100000 and the highest first octet is 11101111. In decimal these two numbers are 224 and 239, respectively. Therefore, the first octet of a class D address will range from 224 to 239.

(a) Enough subnet bits n are needed so that 2ⁿ 2 > = 16,000. There must be enough host bits h remaining so that 2^h 2 > = 700. A subnet mask of 255.255.252.0 provides 16,382 subnets of the class A address, and 1022 host addresses on each subnet. This mask is the only one that works. If one more bit is used for subnetting (255.255.254.0), there will not be enough host addresses. If one less bit is used for subnetting (255.255.248.0), there will not be enough subnets.

(b) Enough subnet bits n are needed so that 2ⁿ 2 > = 500. Enough host bits h must remain so that 2^h 2 > = 100. A subnet mask of 255.255.255.128 provides 510 subnets of the class B address and 126 host addresses on each subnet. Again, this mask is the only one that works.

With six bits of subnetting, a class C address will have 2⁶ 2 = 62 subnets and 2² 2 = 2 host addresses per subnet. With this subnetting scheme, a single class C address can be used for 62 point-to-point links. A point-to-point link requires only two host addressesone for each end of the link.

A class C address with a 28-bit mask will have 14 subnets and 14 host addresses on each subnet. The subnets are derived first.

The subnets are

11111111111111111111111111110000 = 255.255.255.240 (mask)
11000000101010001001001100010000 = 192.168.147.16
11000000101010001001001100100000 = 192.168.147.32
11000000101010001001001100110000 = 192.168.147.48
11000000101010001001001101000000 = 192.168.147.64
11000000101010001001001101010000 = 192.168.147.80
11000000101010001001001101100000 = 192.168.147.96
11000000101010001001001101110000 = 192.168.147.112
11000000101010001001001110000000 = 192.168.147.128
11000000101010001001001110010000 = 192.168.147.144
11000000101010001001001110100000 = 192.168.147.160
11000000101010001001001110110000 = 192.168.147.176
11000000101010001001001111000000 = 192.168.147.192
11000000101010001001001111010000 = 192.168.147.208
11000000101010001001001111100000 = 192.168.147.224

Next, the host addresses for each subnet are derived. The broadcast addresses for each subnet are also shown.

The host addresses for each subnet are

11000000101010001001001100010000 = 192.168.147.16 (subnet)
11000000101010001001001100010001 = 192.168.147.17
11000000101010001001001100010010 = 192.168.147.18
11000000101010001001001100010011 = 192.168.147.19
11000000101010001001001100010100 = 192.168.147.20
11000000101010001001001100010101 = 192.168.147.21
11000000101010001001001100010110 = 192.168.147.22
11000000101010001001001100010111 = 192.168.147.23
11000000101010001001001100011000 = 192.168.147.24
11000000101010001001001100011001 = 192.168.147.25
11000000101010001001001100011010 = 192.168.147.26
11000000101010001001001100011011 = 192.168.147.27
11000000101010001001001100011100 = 192.168.147.28
11000000101010001001001100011101 = 192.168.147.29
11000000101010001001001100011110 = 192.168.147.30
11000000101010001001001100011111 = 192.168.147.31 (broadcast)
11000000101010001001001100100000 = 192.168.147.32 (subnet)
11000000101010001001001100100001 = 192.168.147.33
11000000101010001001001100100010 = 192.168.147.34
11000000101010001001001100100011 = 192.168.147.35
11000000101010001001001100100100 = 192.168.147.36
11000000101010001001001100100101 = 192.168.147.37
11000000101010001001001100100110 = 192.168.147.38
11000000101010001001001100100111 = 192.168.147.39
11000000101010001001001100101000 = 192.168.147.40
11000000101010001001001100101001 = 192.168.147.41
11000000101010001001001100101010 = 192.168.147.42
11000000101010001001001100101011 = 192.168.147.43
11000000101010001001001100101100 = 192.168.147.44
11000000101010001001001100101101 = 192.168.147.45
11000000101010001001001100101110 = 192.168.147.46
11000000101010001001001100101111 = 192.168.147.47 (broadcast)
11000000101010001001001100110000 = 192.168.147.48 (subnet)
11000000101010001001001100110001 = 192.168.147.49
11000000101010001001001100110010 = 192.168.147.50
11000000101010001001001100110011 = 192.168.147.51
11000000101010001001001100110100 = 192.168.147.52
11000000101010001001001100110101 = 192.168.147.53
11000000101010001001001100110110 = 192.168.147.54
11000000101010001001001100110111 = 192.168.147.55
11000000101010001001001100111000 = 192.168.147.56
11000000101010001001001100111001 = 192.168.147.57
11000000101010001001001100111010 = 192.168.147.58
11000000101010001001001100111011 = 192.168.147.59
11000000101010001001001100111100 = 192.168.147.60
11000000101010001001001100111101 = 192.168.147.61
11000000101010001001001100111110 = 192.168.147.62
11000000101010001001001100111111 = 192.168.147.63 (broadcast)
11000000101010001001001101000000 = 192.168.147.64 (subnet)
11000000101010001001001101000001 = 192.168.147.65
11000000101010001001001101000010 = 192.168.147.66
11000000101010001001001101000011 = 192.168.147.67
11000000101010001001001101000100 = 192.168.147.68
11000000101010001001001101000101 = 192.168.147.69
11000000101010001001001101000110 = 192.168.147.70
11000000101010001001001101000111 = 192.168.147.71
11000000101010001001001101001000 = 192.168.147.72
11000000101010001001001101001001 = 192.168.147.73
11000000101010001001001101001010 = 192.168.147.74
11000000101010001001001101001011 = 192.168.147.75
11000000101010001001001101001100 = 192.168.147.76
11000000101010001001001101001101 = 192.168.147.77
11000000101010001001001101001110 = 192.168.147.78
11000000101010001001001101001111 = 192.168.147.79 (broadcast)
11000000101010001001001101010000 = 192.168.147.80 (subnet)
11000000101010001001001101010001 = 192.168.147.81
11000000101010001001001101010010 = 192.168.147.82
11000000101010001001001101010011 = 192.168.147.83
11000000101010001001001101010100 = 192.168.147.84
11000000101010001001001101010101 = 192.168.147.85
11000000101010001001001101010110 = 192.168.147.86
11000000101010001001001101010111 = 192.168.147.87
11000000101010001001001101011000 = 192.168.147.88
11000000101010001001001101011001 = 192.168.147.89
11000000101010001001001101011010 = 192.168.147.90
11000000101010001001001101011011 = 192.168.147.91
11000000101010001001001101011100 = 192.168.147.92
11000000101010001001001101011101 = 192.168.147.93
11000000101010001001001101011110 = 192.168.147.94
11000000101010001001001101011111 = 192.168.147.95 (broadcast)
11000000101010001001001101100000 = 192.168.147.96 (subnet)
11000000101010001001001101100001 = 192.168.147.97
11000000101010001001001101100010 = 192.168.147.98
11000000101010001001001101100011 = 192.168.147.99
11000000101010001001001101100100 = 192.168.147.100
11000000101010001001001101100101 = 192.168.147.101
11000000101010001001001101100110 = 192.168.147.102
11000000101010001001001101100111 = 192.168.147.103
11000000101010001001001101101000 = 192.168.147.104
11000000101010001001001101101001 = 192.168.147.105
11000000101010001001001101101010 = 192.168.147.106
11000000101010001001001101101011 = 192.168.147.107
11000000101010001001001101101100 = 192.168.147.108
11000000101010001001001101101101 = 192.168.147.109
11000000101010001001001101101110 = 192.168.147.110
11000000101010001001001101101111 = 192.168.147.111 (broadcast)
11000000101010001001001101110000 = 192.168.147.112 (subnet)
11000000101010001001001101110001 = 192.168.147.113
11000000101010001001001101110010 = 192.168.147.114
11000000101010001001001101110011 = 192.168.147.115
11000000101010001001001101110100 = 192.168.147.116
11000000101010001001001101110101 = 192.168.147.117
11000000101010001001001101110110 = 192.168.147.118
11000000101010001001001101110111 = 192.168.147.119
11000000101010001001001101111000 = 192.168.147.120
11000000101010001001001101111001 = 192.168.147.121
11000000101010001001001101111010 = 192.168.147.122
11000000101010001001001101111011 = 192.168.147.123
11000000101010001001001101111100 = 192.168.147.124
11000000101010001001001101111101 = 192.168.147.125
11000000101010001001001101111110 = 192.168.147.126
11000000101010001001001101111111 = 192.168.147.127 (broadcast)
11000000101010001001001110000000 = 192.168.147.128 (subnet)
11000000101010001001001110000001 = 192.168.147.129
11000000101010001001001110000010 = 192.168.147.130
11000000101010001001001110000011 = 192.168.147.131
11000000101010001001001110000100 = 192.168.147.132
11000000101010001001001110000101 = 192.168.147.133
11000000101010001001001110000110 = 192.168.147.134
11000000101010001001001110000111 = 192.168.147.135
11000000101010001001001110001000 = 192.168.147.136
11000000101010001001001110001001 = 192.168.147.137
11000000101010001001001110001010 = 192.168.147.138
11000000101010001001001110001011 = 192.168.147.139
11000000101010001001001110001100 = 192.168.147.140
11000000101010001001001110001101 = 192.168.147.141
11000000101010001001001110001110 = 192.168.147.142
11000000101010001001001110001111 = 192.168.147.143 (broadcast)
11000000101010001001001110010000 = 192.168.147.144 (subnet)
11000000101010001001001110010001 = 192.168.147.145
11000000101010001001001110010010 = 192.168.147.146
11000000101010001001001110010011 = 192.168.147.147
11000000101010001001001110010100 = 192.168.147.148
11000000101010001001001110010101 = 192.168.147.149
11000000101010001001001110010110 = 192.168.147.150
11000000101010001001001110010111 = 192.168.147.151
11000000101010001001001110011000 = 192.168.147.152
11000000101010001001001110011001 = 192.168.147.153
11000000101010001001001110011010 = 192.168.147.154
11000000101010001001001110011011 = 192.168.147.155
11000000101010001001001110011100 = 192.168.147.156
11000000101010001001001110011101 = 192.168.147.157
11000000101010001001001110011110 = 192.168.147.158
11000000101010001001001110011111 = 192.168.147.159 (broadcast)
11000000101010001001001110100000 = 192.168.147.160 (subnet)
11000000101010001001001110100001 = 192.168.147.161
11000000101010001001001110100010 = 192.168.147.162
11000000101010001001001110100011 = 192.168.147.163
11000000101010001001001110100100 = 192.168.147.164
11000000101010001001001110100101 = 192.168.147.165
11000000101010001001001110100110 = 192.168.147.166
11000000101010001001001110100111 = 192.168.147.167
11000000101010001001001110101000 = 192.168.147.168
11000000101010001001001110101001 = 192.168.147.169
11000000101010001001001110101010 = 192.168.147.170
11000000101010001001001110101011 = 192.168.147.171
11000000101010001001001110101100 = 192.168.147.172
11000000101010001001001110101101 = 192.168.147.173
11000000101010001001001110101110 = 192.168.147.174
11000000101010001001001110101111 = 192.168.147.175 (broadcast)
11000000101010001001001110110000 = 192.168.147.176 (subnet)
11000000101010001001001110110001 = 192.168.147.177
11000000101010001001001110110010 = 192.168.147.178
11000000101010001001001110110011 = 192.168.147.179
11000000101010001001001110110100 = 192.168.147.180
11000000101010001001001110110101 = 192.168.147.181
11000000101010001001001110110110 = 192.168.147.182
11000000101010001001001110110111 = 192.168.147.183
11000000101010001001001110111000 = 192.168.147.184
11000000101010001001001110111001 = 192.168.147.185
11000000101010001001001110111010 = 192.168.147.186
11000000101010001001001110111011 = 192.168.147.187
11000000101010001001001110111100 = 192.168.147.188
11000000101010001001001110111101 = 192.168.147.189
11000000101010001001001110111110 = 192.168.147.190
11000000101010001001001110111111 = 192.168.147.191 (broadcast)
11000000101010001001001111000000 = 192.168.147.192 (subnet)
11000000101010001001001111000001 = 192.168.147.193
11000000101010001001001111000010 = 192.168.147.194
11000000101010001001001111000011 = 192.168.147.195
11000000101010001001001111000100 = 192.168.147.196
11000000101010001001001111000101 = 192.168.147.197
11000000101010001001001111000110 = 192.168.147.198
11000000101010001001001111000111 = 192.168.147.199
11000000101010001001001111001000 = 192.168.147.200
11000000101010001001001111001001 = 192.168.147.201
11000000101010001001001111001010 = 192.168.147.202
11000000101010001001001111001011 = 192.168.147.203
11000000101010001001001111001100 = 192.168.147.204
11000000101010001001001111001101 = 192.168.147.205
11000000101010001001001111001110 = 192.168.147.206
11000000101010001001001111001111 = 192.168.147.207 (broadcast)
11000000101010001001001111010000 = 192.168.147.208 (subnet)
11000000101010001001001111010001 = 192.168.147.209
11000000101010001001001111010010 = 192.168.147.210
11000000101010001001001111010011 = 192.168.147.211
11000000101010001001001111010100 = 192.168.147.212
11000000101010001001001111010101 = 192.168.147.213
11000000101010001001001111010110 = 192.168.147.214
11000000101010001001001111010111 = 192.168.147.215
11000000101010001001001111011000 = 192.168.147.216
11000000101010001001001111011001 = 192.168.147.217
11000000101010001001001111011010 = 192.168.147.218
11000000101010001001001111011011 = 192.168.147.219
11000000101010001001001111011100 = 192.168.147.220
11000000101010001001001111011101 = 192.168.147.221
11000000101010001001001111011110 = 192.168.147.222
11000000101010001001001111011111 = 192.168.147.223 (broadcast)
11000000101010001001001111100000 = 192.168.147.224 (subnet)
11000000101010001001001111100001 = 192.168.147.225
11000000101010001001001111100010 = 192.168.147.226
11000000101010001001001111100011 = 192.168.147.227
11000000101010001001001111100100 = 192.168.147.228
11000000101010001001001111100101 = 192.168.147.229
11000000101010001001001111100110 = 192.168.147.230
11000000101010001001001111100111 = 192.168.147.231
11000000101010001001001111101000 = 192.168.147.232
11000000101010001001001111101001 = 192.168.147.233
11000000101010001001001111101010 = 192.168.147.234
11000000101010001001001111101011 = 192.168.147.235
11000000101010001001001111101100 = 192.168.147.236
11000000101010001001001111101101 = 192.168.147.237
11000000101010001001001111101110 = 192.168.147.238
11000000101010001001001111101111 = 192.168.147.239 (broadcast)

This solution shows a shorter technique than the last solution in which every host address of every subnet was written out.

A class C address with a 29-bit mask means that there will be 30 subnets and 6 host addresses on each subnet.

The subnets are

11111111111111111111111111111000 = 255.255.255.248 (mask)
11000000101010001001001100001000 = 192.168.147.8
11000000101010001001001100010000 = 192.168.147.16
11000000101010001001001100011000 = 192.168.147.24
11000000101010001001001100100000 = 192.168.147.32
11000000101010001001001100101000 = 192.168.147.40
11000000101010001001001100110000 = 192.168.147.48
11000000101010001001001100111000 = 192.168.147.56
11000000101010001001001101000000 = 192.168.147.64
11000000101010001001001101001000 = 192.168.147.72
11000000101010001001001101010000 = 192.168.147.80
11000000101010001001001101011000 = 192.168.147.88
11000000101010001001001101100000 = 192.168.147.96
11000000101010001001001101101000 = 192.168.147.104
11000000101010001001001101100000 = 192.168.147.112
11000000101010001001001101111000 = 192.168.147.120
11000000101010001001001110000000 = 192.168.147.128
11000000101010001001001110001000 = 192.168.147.136
11000000101010001001001110010000 = 192.168.147.144
11000000101010001001001110011000 = 192.168.147.152
11000000101010001001001110100000 = 192.168.147.160
11000000101010001001001110101000 = 192.168.147.168
11000000101010001001001110110000 = 192.168.147.176
11000000101010001001001110111000 = 192.168.147.184
11000000101010001001001111000000 = 192.168.147.192
11000000101010001001001111001000 = 192.168.147.200
11000000101010001001001111010000 = 192.168.147.208
11000000101010001001001111011000 = 192.168.147.216
11000000101010001001001111100000 = 192.168.147.224
11000000101010001001001111101000 = 192.168.147.232
11000000101010001001001111110000 = 192.168.147.240

Next, the broadcast addresses of each subnet are derived by setting the host bits of each subnet to all ones.

The subnet broadcast addresses are

11000000101010001001001100001111 = 192.168.147.15
11000000101010001001001100010111 = 192.168.147.23
11000000101010001001001100011111 = 192.168.147.31
11000000101010001001001100100111 = 192.168.147.39
11000000101010001001001100101111 = 192.168.147.47
11000000101010001001001100110111 = 192.168.147.55
11000000101010001001001100111111 = 192.168.147.63
11000000101010001001001101000111 = 192.168.147.71
11000000101010001001001101001111 = 192.168.147.79
11000000101010001001001101010111 = 192.168.147.87
11000000101010001001001101011111 = 192.168.147.95
11000000101010001001001101100111 = 192.168.147.103
11000000101010001001001101101111 = 192.168.147.111
11000000101010001001001101100111 = 192.168.147.119
11000000101010001001001101111111 = 192.168.147.127
11000000101010001001001110000111 = 192.168.147.135
11000000101010001001001110001111 = 192.168.147.143
11000000101010001001001110010111 = 192.168.147.151
11000000101010001001001110011111 = 192.168.147.159
11000000101010001001001110100111 = 192.168.147.167
11000000101010001001001110101111 = 192.168.147.175
11000000101010001001001110110111 = 192.168.147.183
11000000101010001001001110111111 = 192.168.147.191
11000000101010001001001111000111 = 192.168.147.199
11000000101010001001001111001111 = 192.168.147.207
11000000101010001001001111010111 = 192.168.147.215
11000000101010001001001111011111 = 192.168.147.223
11000000101010001001001111100111 = 192.168.147.231
11000000101010001001001111101111 = 192.168.147.239
11000000101010001001001111110111 = 192.168.147.247

Finally, the host addresses for each subnet are derived. They will be all addresses between the subnet addresses and the subnet broadcast addresses.

Subnet	Broadcast	Host Addresses
192.168.147.8	192.168.147.15	192.168.147.9192.168.147.14
192.168.147.16	192.168.147.23	192.168.147.17192.168.147.22
192.168.147.24	192.168.147.31	192.168.147.25192.168.147.30
192.168.147.32	192.168.147.39	192.168.147.33192.168.147.38
192.168.147.40	192.168.147.47	192.168.147.41192.168.147.46
192.168.147.48	192.168.147.55	192.168.147.49192.168.147.54
192.168.147.56	192.168.147.63	192.168.147.57192.168.147.62
192.168.147.64	192.168.147.71	192.168.147.65192.168.147.70
192.168.147.72	192.168.147.79	192.168.147.73192.168.147.78
192.168.147.80	192.168.147.87	192.168.147.81192.168.147.86
192.168.147.88	192.168.147.95	192.168.147.89192.168.147.94
192.168.147.96	192.168.147.103	192.168.147.97192.168.147.102
192.168.147.104	192.168.147.111	192.168.147.105192.168.147.110
192.168.147.112	192.168.147.119	192.168.147.113192.168.147.118
192.168.147.120	192.168.147.127	192.168.147.121192.168.147.126
192.168.147.128	192.168.147.135	192.168.147.129192.168.147.134
192.168.147.136	192.168.147.143	192.168.147.137192.168.147.142
192.168.147.144	192.168.147.151	192.168.147.145192.168.147.150
192.168.147.152	192.168.147.159	192.168.147.153192.168.147.158
192.168.147.160	192.168.147.167	192.168.147.161192.168.147.166
192.168.147.168	192.168.147.175	192.168.147.169192.168.147.174

A class B address with a 20-bit mask will have 14 subnets and 4,094 host addresses on each subnet.

The subnets are

11111111111111111111000000000000 = 255.255.240.0 (mask)
10101100000100000001000000000000 = 172.16.16.0
10101100000100000010000000000000 = 172.16.32.0
10101100000100000011000000000000 = 172.16.48.0
10101100000100000100000000000000 = 172.16.64.0
10101100000100000101000000000000 = 172.16.80.0
10101100000100000110000000000000 = 172.16.96.0
10101100000100000111000000000000 = 172.16.112.0
10101100000100001000000000000000 = 172.16.128.0
10101100000100001001000000000000 = 172.16.144.0
10101100000100001010000000000000 = 172.16.160.0
10101100000100001011000000000000 = 172.16.176.0
10101100000100001100000000000000 = 172.16.192.0
10101100000100001101000000000000 = 172.16.208.0
10101100000100001110000000000000 = 172.16.224.0

The subnet broadcast addresses are

10101100000100000001111111111111 = 172.16.31.255
10101100000100000010111111111111 = 172.16.47.255
10101100000100000011111111111111 = 172.16.63.255
10101100000100000100111111111111 = 172.16.79.255
10101100000100000101111111111111 = 172.16.95.255
10101100000100000110111111111111 = 172.16.111.255
10101100000100000111111111111111 = 172.16.127.255
10101100000100001000111111111111 = 172.16.143.255
10101100000100001001111111111111 = 172.16.159.255
10101100000100001010111111111111 = 172.16.175.255
10101100000100001011111111111111 = 172.16.191.255
10101100000100001100111111111111 = 172.16.207.255
10101100000100001101111111111111 = 172.16.223.255
10101100000100001110111111111111 = 172.16.239.255

Using the derived subnet and broadcast addresses, the host addresses are as follows.

Subnet	Broadcast	Host Addresses
172.16.16.0	172.16.31.255	172.16.16.1172.16.31.254
172.16.32.0	172.16.47.255	172.16.32.1172.16.47.254
172.16.48.0	172.16.63.255	172.16.48.1172.16.63.254
172.16.64.0	172.16.79.255	172.16.64.1172.16.79.254
172.16.80.0	172.16.95.255	172.16.80.1172.16.95.254
172.16.96.0	172.16.111.255	172.16.96.1172.16.111.254
172.16.112.0	172.16.127.255	172.16.112.1172.16.127.254
172.16.128.0	172.16.143.255	172.16.128.1172.16.143.254
172.16.144.0	172.16.159.255	172.16.144.1172.16.159.254
172.16.160.0	172.16.175.255	172.16.160.1172.16.175.254
172.16.176.0	172.16.191.255	172.16.176.1172.16.191.254
172.16.192.0	172.16.207.255	172.16.192.1172.16.207.254
172.16.208.0	172.16.223.255	172.16.208.1172.16.223.254
172.16.224.0	172.16.239.255	172.224.16.1172.16.239.254