11. (12 points) In the equation $\overline{\mathrm{ABCD}}+E \times F \times G \times H=2011$, $A, B, C, D, E, F, G, H$ represent different digits from $1 \sim 8$ (different letters represent different digits), then the four-digit number $\overline{\mathrm{ABCD}}=$ $\qquad$

将上面的文本翻译成英文，请保留源文本的换行和格式，直接输出翻译结果。
【Solution】Solution: According to the problem, we have:
Since $E \times F \times G \times H \geqslant 1 \times 2 \times 3 \times 4=24$, then $A=1$, so at least one of $E, F, G, H$ is even. If 5 is in $E, F, G, H$, then the unit digit of $E \times F \times G \times H$ is $0, D=1$ which is a contradiction, so 5 is in $B, C$, $D$.

Now we determine that two of the digits in $A, B, C, D$ are 1 and 5.
Then consider the remainder of each number in this addition equation when divided by 3. The remainder of 2011 divided by 3 is $1, E \times F \times G \times H$ divided by 3 has two cases, it is 0 or not 0.
When the remainder of $E \times F \times G \times H$ divided by 3 is 0.
Then the remainder of $\overline{\mathrm{ABCD}}$ divided by 3 is 1, because $A, B, C, D$ have the digits 1 and 5, so the remainder of the sum of the remaining two digits divided by 3 is 1, which could be $(3,4),(3,7),(6,4),(6,7),(2,8)$;
(1) If it is 3 and 4, then $E \times F \times G \times H=2 \times 6 \times 7 \times 8=672$, then $D$ is 9 which is impossible.
(2) If it is 3 and 7, then $E \times F \times G \times H=2 \times 4 \times 6 \times 8=384, \overline{\mathrm{ABCD}}=2011-336=1675$, contradiction.
(3) If it is 6 and 4, then $E \times F \times G \times H=2 \times 3 \times 7 \times 8=336, \overline{\mathrm{ABCD}}=2011-336=1675$. Contradiction.
(4) If it is 6 and 7, then $E \times F \times G \times H=2 \times 3 \times 4 \times 8=192, D$ is 9 which is impossible.
(5) If it is 2 and 8, then $E \times F \times G \times H=3 \times 4 \times 6 \times 7=504, D$ is 7 which is a contradiction.

When the remainder of $E \times F \times G \times H$ divided by 3 is not 0, it means that 3 and 6 are not in $E \times F \times G \times H$, so $E \times$ $F \times G \times H=2 \times 4 \times 7 \times 8=448$.
$\overline{\mathrm{ABCD}}=2011-448=1563$. This satisfies the problem.
Therefore, the answer is: 1563.