Numbers have been represented in a variety of different methods throughout history. For example, if you look at the face of some clocks, you may see that six o’clock is designated by `VI`

, the Roman Numeral for `6`

.

The most successful system of numbering is called the decimal system, from the Latin root **dec-** meaning *set of ten* or *having a base of ten*.

Although the exact origins of this system are unknown, it is clear that it began with counting on our fingers and later evolved into substituting the Hindu-Arab characters of `0`

, `1`

, `2`

, `3`

, `4`

, `5`

, `6`

, `7`

, `8`

, and `9`

for fingers in order to perform larger operations.

In the decimal system, each digit can be represented by a multiple of a power of ten and added together with the other digits. Let’s look at the number `305`

.

Starting at the right and moving left, the first column is the ones digit. The digit in this place value is `5`

.

**5 times 10 ^{0} =**

`5`

The next digit, in the ten’s column, is `0`

.

**0 times 10 ^{1} =**

`0`

Finally, the `3`

is in the hundred’s column:

**3 times 10 ^{2} =**

`300`

By adding each column together, we get our total value:

5 + 0 + 300 = 305.

The binary system is very similar to the decimal system except it uses a base of two and only two digits, `0`

and `1`

. With the provided table we can use the same technique to evaluate `100110001`

, which is `305`

in binary. Try it out.

In binary, the digit that is farthest to the right is called the *Least Significant Bit* (LSB) and the left-most digit is called the *Most Significant Bit* (MSB).

### Instructions

Take a look at the visualization to the right to see the numbers 1-10 converted to binary.