Frank wrote:i thought 192.0.2.255 would be the network range broadcast address
Well this would be true if you had 192.0.2.0/24. But the network given is 192.0.2.0/23, which means that
1) network address is 192.0.2.0
2) broadcast address is 192.0.3.255
3) the valid range of assignable addresses is 192.0.2.1 - 192.0.3.254
So 192.0.2.255 is a valid address. Likewise, 192.0.3.0 is a valid address, too.
Here is a detailed explanation:
192.0.2.0 is 11000000 00000000 00000010 00000000 in binary
the mask is /23 = 255.255.254.0 = 11111111 11111111 11111110 00000000
Let's line this up
11000000 00000000 0000001|0 00000000 - network address
11111111 11111111 1111111|0 00000000 - subnet mask
Now we can get broadcast address by filling the right part of network address with 1s:
11000000 00000000 0000001|1 11111111 - broadcast address = 192.0.3.255