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6,122 PointsWhy is 00000111 not equal to 6?
Why is 00000111 not equal to 6 ?
5 Answers
Ken Alger
Treehouse TeacherJasmine;
Welcome to Treehouse!
Perhaps the following chart will help somewhat.
Binary | Decimal |
---|---|
0 | 0 |
1 | 1 |
10 | 2 |
11 | 3 |
100 | 4 |
101 | 5 |
110 | 6 |
111 | 7 |
If there is a 1
in the right most digit in binary, it will be an odd number in base 10.
Hope it helps,
Ken
Amber Cyr
19,699 Pointshere 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!
Tim Larson
Full Stack JavaScript Techdegree Student 13,696 PointsHi 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!
Unsubscribed User
6,122 PointsThanks
miikis
44,957 PointsHere'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:
\ Base 10 \ | \ Base 10 \ | \ Base 10 \ | \ Base 2 \ | \ Base 2 \ |
---|---|---|---|---|
15 = | (1 * 10^1) + (5 * 10^0) = | 10 + 5 = | 1111 = | (1 * 2^3) + (1 * 2^2) + (1 * 2^1) + (1 * 2^0) |
10 = | (1 * 10^1) + (0 * 10^0) = | 10 + 0 = | 1010 = | (1 * 2^3) + (0 * 2^2) + (1 * 2^1) + (0 * 2^0) |
6 = | (6 * 10^0) = | 6 = | 110 = | (1 * 2^2) + (1 * 2^1) + (0 * 2^0) |