Write the smallest 4-digit number having distinct digits.

The digits available are 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.

For the smallest 4-digit number with distinct digits, the thousands place cannot be 0. So, the smallest non-zero digit (1) is placed at the thousand's place. Then arrange the remaining smallest digits in ascending order:

Thousands place: 1

Hundreds place: 0

Tens place: 2

Ones place: 3

Hence, the smallest 4-digit number having distinct digits is 1,023.