About the problem of the subnet mask appearing odd in the subnet partition

An odd number of subnet masks appear on subnetting
1.0.1.0--1.0.3.255 Fujian province Telecom converted to 1.0.1.0/24--1.0.2.0/23

Above is an IP segment, after the molecular network to get behind the two network segments and subnet mask, if the general method,

Change two IP to binary for XOR budget
00000001.00000000.00000001.00000000
00000001.00000000.00000011.11111111

The resulting subnet mask is

11111111.11111111.11111101.00000000
255.255.253.0

But the third paragraph clearly does not conform to successive one and 0 consecutive rules, but do not know the top of the divided into two segments of the basis is what, looking for expert answers, online, etc., thank you!

------Solution--------------------
Do you want to understand the principle or a specific point of demand, say first.
------Solution--------------------
1.0.1.0--1.0.3.255 by 24-bit mask (c-type URL), a total of 3 network segments

11111111 11111111 11111111 00000000 Mask

00000001 00000000 00000001 00000000 Network Segment 1
00000001 00000000 00000010 00000000 Network Segment 2
00000001 00000000 00000011 00000000 Network Segment 3

When the mask is 23 bits
11111111 11111111 11111110 00000000 Mask
Three segments and (red part)
00000001 00000000 00000001 00000000 Network Segment 1
00000001 00000000 00000000 00000000 Result 1
00000001 00000000 00000010 00000000 Network Segment 2
00000001 00000000 00000010 00000000 Result 2
00000001 00000000 00000011 00000000 Network Segment 3
00000001 00000000 00000010 00000000 Result 3

Obviously, result 2 and result 3 are equal, so it is a network segment

