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I'm learning subnetting at the moment and I'm unsure whether this is considered a valid IP address.

150.16.5.255/21

My teacher asserts that this is invalid because it is a broadcast address of one of the networks within a subnet, but my instincts tell me that the broadcast won't be until 150.16.7.255 at the end of the first subnet network.

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It is a perfectly valid IP address on the network 150.16.0.0/21. The host component of the address 101.11111111 is neither all zeros, or all ones.

$ ipcalc 150.16.5.255/21
Address:   150.16.5.255         10010110.00010000.00000 101.11111111
Netmask:   255.255.248.0 = 21   11111111.11111111.11111 000.00000000
Wildcard:  0.0.7.255            00000000.00000000.00000 111.11111111
=>
Network:   150.16.0.0/21        10010110.00010000.00000 000.00000000
HostMin:   150.16.0.1           10010110.00010000.00000 000.00000001
HostMax:   150.16.7.254         10010110.00010000.00000 111.11111110
Broadcast: 150.16.7.255         10010110.00010000.00000 111.11111111
Hosts/Net: 2046
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1

You are correct, 150.16.7.255 is the broadcast address for the 150.16.0.0/21 subnet. 150.16.5.255 is a valid IP for a host on that subnet.

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