According to question, following cases arrises nine digit number (less than 2 × 108) having only digits 1 and 2 = 28 Eight digit number (less than 2 × 108) having only digits 1 and 2 = 28 Similarly, Seven digit numbers = 27 Six digit numbers = 26 , Five digit numbers = 25 , Four digit numbers = 24 , Three digit numbers = 23 , Two digit numbers = 22 and One digit numbers = 2 So, number of all such natural numbers = 2 + 22+23+24+25+26+27+28 = 2 + 4 + 8 + 16 + 32 + 64 + 128 + 256 + 256 = 766