Which one of the following CIDR prefixes exactly represents the range of IP addresses 10.12.2.0 to 10.12.3.255?

We are given the IP address range:

• Start IP: 10.12.2.0

• End IP: 10.12.3.255

1. Total number of addresses: The range covers two /24 subnets (10.12.2.0/24 and 10.12.3.0/24), which gives:

   $$N = 256 + 256 = 512 = 2^9 \text{ addresses}$$

2. Host bits and Prefix length: Since $2^h = 512$, the number of host bits is $h = 9$. The prefix length is:

   $$\text{Prefix Length} = 32 - 9 = 23$$

3. Network Prefix Alignment: Converting the third octet to binary:

   • $2 = 00000010_2$

   • $3 = 00000011_2$

   For a $/23$ prefix, the first 7 bits of the 3rd octet are fixed as network bits ($0000001_2$), and the last bit is a host bit. Thus, the base network address is:

   $$10.12.2.0/23$$

Hence, the correct prefix is 10.12.2.0/23, which corresponds to option (A).