Yes it will work. But the delay increases proportionately with the number of levels in turn number of Gate braches, as shown in the diagram..There are many ways you can implement an adder..half adder, full adder, but if the delay should be less 'Carry look ahead adder' will be the best and simple choice
It will add n bit m input system in an efficient way by generating the carry before it is actually generated by the normal adder. As it is generating the carry ahead, nth adder need not wait for n-1th carry, so the system will be fast..
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