In our base-10 system, the positions (from right to left) correspond to "number of 1s", "number of 10s", "number of 100s", and so on, where the value of each position is **10** times the previous one.

Binary, or base 2, uses only the digits 0 and 1. Each position corresponds to "number of 1s", "number of 2s", "number of 4s", "number of 8s", and so on. The value of each position is **2** times the previous one.

The number above expressed in base 10 is $8 + 1 = 9 ,$ since there is one 8 and one 1.

**What is the value (in base 10) of the binary number 10000?**

Which binary number is larger?

**1** or 11101**1**), then it is $\text{\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_}.$

What is the result (in binary) of multiplying the binary number 1100 by the binary number 10?

Here are the binary numbers listed starting from 2. Consider **the second from the last digit**.

10,11, 100, 101, 110, 111, 1000, 1001, 1010, 1011, 1100, 1101, 1110, 1111, ...

Notice the pattern 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, ...

**Does this pattern continue for all positive integers?**