what number is represented by the byte 00001000

Michael gave a great explanation of this, I just want to add this visual representation for proof which may also help:

Binary Place       Binary Number      Digit and binary number multiplied (Binary Digit * Binary Number)
2^7  (128)         0                  0 (128 * 0)
2^6  (64)          0                  0 (64 * 0)
2^5  (32)          0                  0 (32 * 0)
2^4  (16)          0                  0 (16 * 0)
2^3  (8)           1                  8 (8 * 1)    like what michael said, there is only a single 1, and that 1 is in the 8 place, so the number is 8
2^2  (4)           0                  0 (4 * 0)
2^1  (2)           0                  0 (2 * 0)
2^0  (1)           0                + 0 (1 * 0)
                                  ----------------
                                      8

There's a 0 in the 1's, 2's, and 4's place, then a 1 in the 8's place, and 0s in the rest. adding up all of the 1s present, you get 8.

The short answer: 8

The long answer:

Naturally, humans count in base-10. That means that each place represents a number 0-9. Therefore, in each place, the highest number you can write is 9. Binary is base-2. That means the highest number you can write in each place is 1. That means each place means something different, too. To have a 1 in a place is to have the value be worth 1 more than if all the other places before it had a 1 in it, or double the space immediately before it. Here's an example:

In base-2, 1 is worth the same thing as base-10. However, 10 in base-2 is 2 in base-10. 11 is 3, 100 is 4, 101, is 5, 110 is 6, 111 is 7, and so on. You just need to know what place each 1 represents, and then add together all the places that have a 1 in them.

In this case, there is only a single 1, and that 1 is in the 8 place, so the number is 8.