1. Write the smallest four-digit number in which all digits are different.
1. According to the problem, to record a four-digit number, four different digits should be used. They can be chosen from $0,1,2,3,4,5,6,7,8,9$.

The smallest digit in the thousands place can be $1: 1^{* * *}$.

The smallest digit in the hundreds place can be $0: 10^{* *}$.

Since we have already used 1 and 0, the digit in the tens place will be $2: 102 *$.

As a result, we get the number 1023.

Answer: 1023.