binary multiplier logic gates is a shift register required

Hi

I am just looking at binary multipliers like this 2 bit one on wiki:
http://en.wikipedia.org/wiki/File:Binary_multi1.jpg

I was wondering if binary multipliers would normally have a shift register?

I am looking at examples and they don't seem to have d flip flops which I thought would make up a shift register.

So my questions is do binary multipliers just use full adders and other additional logic gates, or do they require shift registers when they get upwards of 2 bit multiplication?

Thanks for any help