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Treehouse offers a seven day free trial for new students. Get access to thousands of hours of content and join thousands of Treehouse students and alumni in the community today. # what number is represented by the byte 00000111

## 0000001 => 1

This is equal 1 because 2 to the 0th power is one, and there's nothing to add to that.

## 0000011 => 3

You might think this should be 2, but don't get mixed up! This is the same as saying: "2 to the first power plus 2 to the 0th power"

Or, in math, you could represent it as:

#### 2^1 + 2^0

This makes it three. Two to the first power is 2, and you are adding that to 2 to the 0th power which is 1.

## 0000111 => 7

Wow, this is getting a little confusing...

Anyway, this is basically saying:

#### 2^2 + 2^1 + 2^0

Which is the same as:

##### 4 + 2 + 1

Which, of course is 7. Just remember binary has a base of 2 and the exponent always depends on where the 1 is. If the last number is a 1, that means the exponent is 0. If the second-last number is 1, then that means the exponent is 1. And so on...

I hope this helps Good luck! ~Alex

Don't worry; I don't think you will have to deal with binary for the rest of your career after this Lol