OK. Here's one where the carry isn't present:-

a=8
b=10
m=13
B=R=16
n=1
mprime = (-m)^-1 (mod 16) = 11

x=a
y=bR (mod m)=160 mod 13 = 4

u=x*y*m' (mod B) = 8*4*11 mod 16 = 0

Ahhh....is this why?