Convert binary to IP-address

This restriction on CIDR was created to forbid that an arbitrary block could be created, let's see an example:

Suppose that we have the full block 192.168.1.0/24 and we want to subnet it with /27

/27 means that from the 32 bits of the address, 27 are network, and 5 are host, then we have 2^5 addresses per subnet.

The subnets are:

First Address    Last Octet  Last Octet 
                             in decimal /32

192.168.1.0      000 00000       0
192.168.1.32     001 00000       1
192.168.1.64     010 00000       2
192.168.1.96     011 00000       3
192.168.1.128    100 00000       4
192.168.1.160    101 00000       5
192.168.1.192    110 00000       6
192.168.1.224    111 00000       7

The first address divided by the number of addresses per subnet is always an integer without decimals, and that is possible because the last k bits are 0.

It makes impossible to have a block starting on 192.168.1.133, for example, because 133/32 = 4.15625

It is because IP addresses are binary numbers. The text representation is simply to make it easier for humans to read. RFC 4291, IP Version 6 Addressing Architecture explains the 10-bit prefix:

2.5.6. Link-Local IPv6 Unicast Addresses

Link-Local addresses are for use on a single link. Link-Local addresses have the following format:

|   10     |
|  bits    |         54 bits         |          64 bits           |
+----------+-------------------------+----------------------------+
|1111111010|           0             |       interface ID         |
+----------+-------------------------+----------------------------+

Link-Local addresses are designed to be used for addressing on a single link for purposes such as automatic address configuration, neighbor discovery, or when no routers are present.

Routers must not forward any packets with Link-Local source or destination addresses to other links.

You can break IPv6 prefixes on any bit boundary, just like you can with IPv4 prefixes, although the recommendation is to break IPv6 prefixes on nibble (hexadecimal character, four-bit) boundaries, it is not a requirement. Other IPv6 ranges break on non-nibble boundaries, too. For example the ULA addressing range is fc00::/7.

Before you ask why it isn't fe80::/64, see the answer to this question.