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You might have missed that M is also the input carry C$_{0}$

A = 1 1 0 0 

B = 1 0 0 0 

M = 1 gives bit-wise XOR of 1 with B

i.e

B = 0 1 1 1

Now to Add

C   1 1 1

A   1 1 0 0

B   0 1 1 1

C            1


   1  0 1 0 0

C$_{4}$S$_{3}$S$_{2}$S$_{1}$S$_{0}$

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