The smallest 4-digit number having distinct digits is

1. 1234

2. 1023

3. 1002

4. 3210

For the smallest 4-digit number with distinct digits, the thousand's place must be the smallest non-zero digit (1). Then the remaining digits in ascending order are 0, 2, 3.

So, the smallest 4-digit number with distinct digits = 1,023.

(Note: 1,002 has the digit 0 repeated, so its digits are not all distinct.)

Hence, option 2 is the correct option.