Unit Adder (4-2 compressor) in Booth-Wallace multiplier

Could anyone tell me a little more detail of the unit adder (4-2
compress)? The logic in M Nagamatsu's paper is different than some
articles on the website. The Cout should only depends on 4 input bit,
rather on Cin. From Nagamatsu's paper,

Cout = (x0 or x1) and (x3 or x3). 

This means if input X = (1100), then Cout is '0', while if the input
is (1010), then Cout is 1. Shouldn't all input bits have basic
property of commutative, ie. a+b = b+a?

Thank you very much in advance.

James Shay