Why is 00000111 not equal to 6?

here is an easy way to look at it (2^num means 2 to the power of num)

2^7  2^6  2^5  2^4  2^3  2^2  2^1  2^0
0    0    0    0    0    1    1    1

2^2 + 2^1 + 2^0 = 4 + 2 + 1 = 7

Binary is in base 2 and the bit count starts at 0 (8 bits which start count at 0 so it ends at 2^7 not 2^8!) you are only worried about the bits with 1s in them. (0's mean "off") so you just add those. Another example:

2^7  2^6  2^5  2^4  2^3  2^2  2^1  2^0
0    0    1    0    1    0    0    0

2^5 + 2^3 = 32 + 8 = 40

Hope this helps!

Hi Jasmine,

When working with binary it's imperative to use the base 2 paradigm. This dictates that each slot from the right is a raised power of 2. For example, in the instance of '00000111' you can think of it as having 1 instance of 2 to the 0 power which equals 1, PLUS 2 to the 1st power which equals 2, PLUS 2 to the 2nd power which equals 4. In essence, 00000111 means 1+2+4 which would return 7. It may be a little bit hard to grasp at first, but I'm sure you'll understand with more practice.

Good luck to you!

Thanks

Here's a video to supplement the other answers here.

Basically, in regards to Base 2, every time you add a non-zero digit on the left, you're adding an incremented power of 2. In Base 10, the way we normally count, every time you add a non-zero digit on the left, you're adding an incremented power of 10. Here's a table (in really small font! Idk what that's about...) to illustrate the Base 10 to Base 2 conversion for the numbers 15, 10 and 6: