Write the smallest eight-digit number using four different digits.

For the smallest 8-digit number using exactly four different digits, the digit at the highest place (crores) cannot be 0. So, the smallest non-zero digit (1) is placed at the highest place.

Use 0 in as many remaining positions as possible. To have exactly four different digits in total, we need two more different digits besides 1 and 0. The smallest such digits are 2 and 3.

Total digits used: 1, 0, 0, 0, 0, 0, 2, 3 — four different digits (1, 0, 2, 3).

Arranging the digits with 1 at the highest place and the rest in ascending order:

1, 0, 0, 0, 0, 0, 2, 3.

Hence, the smallest 8-digit number using four different digits is 1,00,00,023.