Sequence of binary numbers from the decimal system

Write the numbers in decimal system sequentially.

0, 1, 2, 3, ..... 9, 10, 11, 12, ..... 99, 100, 101, 102, 103,

.... 109, 110, 111, 112, 113, .... 999, 1000, 1001, 1002,

..... 1009, 1010, 1011, 1012, .... 1099, 1100, 1101, 1102,

..... 1109, 1110, 1111, 1112, ..... 9999, 10000, 10001, ......
Now retain numbers containing 0 and 1 only

(i.e, scratch out all the numbers containing any of the digits 2 to 9).

0, 1, 10, 11, 100, 101, 110, 111, 1000, 1001, 1010, 1011, 1100, 1101, 1110, 1111, 10000, 10001,........

The above series is the numbers in sequence in the binary number system.