Python 2, 140 bytes
def f(n,k):s=[0]+[int('73673557770e0d93bf0fb0'[d::11],16)for d in map(int,`n`)]+[0];return sum(bin(x^y).count('1')for x,y in zip(s,s[1:]))*k
def f(n,k):s=[0]+[int('73673557770e0d93bf0fb0'[d::11],16)for d in map(int,`n`)]+[0];return sum(bin(x^y).count('1')for x,y in zip(s,s[1:]))*k