Actually, 1111111 is 127...we haven't actually been counting right.
Binary is no different than decimal, except that instead of each 'column' having numbers from 0 to 9, it can only have from 0 to 1 before you add a new column. So 0 1 is easy, then add "1 + 1" and just like when you add 1 to 9 in decimal, you've reached the end for one column, so you have to move to the next column (carry the one, just like in grade school :smile:) so "1 + 1 = 10" (2) 10 + 1 = 11 (3) (3) 11 + 1 = 100 (4, carry the one twice) (4) 100 + 1 = 101 (5) (5) 101 + 1 = 110 (6, carry the one once) (6) 110 + 1 = 111 (7) (7) 111 + 1 = 1000 (8, carry the one three times) (8) 1000 + 1 = 1001 (9) (9) 1001 + 1 = 1010 (10, carry the one once)
Its no different than decimal, but instead of going all the way to 9 before getting to 10, you only go to 1.
The same rules apply to other bases, such as Octal (base 8, so: 0, 1, 2, 3, 4, 5, 6, 7, 10, 11, 12, 13, 14, 15, 16, 17, 20, ...) and Hexidecimal (base 16, use letters A-F once you run out of numbers: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 1A, 1B, 1C, 1D, 1E, 1F, 20). It's just like counting in decimal, you just stop each column at a different number.
Comments
I'm using binary. :wink:
11
hehe
You if the last number is a 1, then you add a 0 to the right hand side. If the last number is a 0 make that number a 1.
sooo...
1
10
11
110
111
1110
1111
11110
11111
etc.
111
1110
I sure screwed this thread up... whoops. But we've all learned a valuable and useful message about binary. :wink:
anyways...
2 !
there! i fixed it!
or
4!
6!
Binary is no different than decimal, except that instead of each 'column' having numbers from 0 to 9, it can only have from 0 to 1 before you add a new column. So
0
1
is easy, then add "1 + 1" and just like when you add 1 to 9 in decimal, you've reached the end for one column, so you have to move to the next column (carry the one, just like in grade school :smile:) so "1 + 1 = 10"
(2) 10 + 1 = 11 (3)
(3) 11 + 1 = 100 (4, carry the one twice)
(4) 100 + 1 = 101 (5)
(5) 101 + 1 = 110 (6, carry the one once)
(6) 110 + 1 = 111 (7)
(7) 111 + 1 = 1000 (8, carry the one three times)
(8) 1000 + 1 = 1001 (9)
(9) 1001 + 1 = 1010 (10, carry the one once)
Its no different than decimal, but instead of going all the way to 9 before getting to 10, you only go to 1.
The same rules apply to other bases, such as Octal (base 8, so: 0, 1, 2, 3, 4, 5, 6, 7, 10, 11, 12, 13, 14, 15, 16, 17, 20, ...) and Hexidecimal (base 16, use letters A-F once you run out of numbers: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 1A, 1B, 1C, 1D, 1E, 1F, 20). It's just like counting in decimal, you just stop each column at a different number.
so to reset this on the right track, here's 7:
111
isn't this fun :smile:
7!!!
8!
Thanks for explaining it Manick, I didn't have the patience to go through all that. :wink:
this thread would get uber confusing if it were to go decimal -> binary -> hexadecimal -> decimal.. pattern
B Hex
13 Octal
11 Decimal
:smile: