What is a binary? How do you work them out?

Question

I can't find the logic in them, how do you do it?

Answer 1

remember when you first started learning to count, you were told about the units column and the tens column and the hundreds column and the thousands, so on.
well, did you ever notice that the units column is 10^0 and the tens column is 10^1 and the hundreds column is 10^2 and the thousands is 10^3?
now imagine, rather than counting to 10, you count to 2 instead before moving into the next column, so the units column is 2^0 and remains units, the tens column is 2^1 and now becomes the twos column and the hundreds now become 2^2... a fours column and the thousands become 2^3, an eights column.
so now lets go back to the decimal base (using tens and hundreds, etc)
100 | 10 | 1| (these are the columns)
----------------
2 | 3 | 0| (this is the number we are given, 230)
so this means we have 2 hundreds, 3 tens and 0 units, which makes 2 hundred and thirty in total... 230
now lets try out the base two (aka binary, the columns with 2,4 and 8):
8 | 4 | 2 | 1 | (these are the columns again)
-----------------------
1 | 0 | 1 | 0 | (this is the number we are given, 1010 in binary)
well this is the same as one eight, 0 fours, one two, and 0 ones, add it up to get 10 in our normal decimal system.
now you might wonder... WHY is it always a 1 or a 0 in binary, well, the same reason once we get to a 9 in decimal we switch into the next column put a one there.
Hope that helps :)

Answer 2

Binary is base2.

If you understand number bases you can understand binary.

Decimal = Base 10:

0 1 2 3 4 5 6 7 8 9 10

1111 = 10^3 + 10^2 + 10^1 + 10^0

Hexadecimal = Base 16:

0 1 2 3 4 5 6 7 8 9 A B C D E F 10

1111 = 16^3 + 16^2 + 16^1 + 16^0

Binary = Base 2:

0 1 10

1111 = 2^3 + 2^2 + 2^1 +2^0

Answer 3

It's quite simple once you get the hang of it.

On a sheet of paper, write:

8 4 2 1

Say you want to express the number 13 in binary. Imagine you can only use each of the above numbers (8,4,2,1) once to reach that total.

There's only one combination that will reach that amount: An 8, a 4 and a 1.

8 4 2 1
1 1 0 1

So in binary, the number 13 is 1101.

To calculate larger numbers, start off with something like:

128 64 32 16 8 4 2 1

(ie doubling the number each time)

Answer 4

Binary refers to the Base 2 counting system. It has only 2 numbers used--0 and 1. You start counting from the right with the "ones" place as 0, and the "twos" place is 1. To count to 10, it goes like this: 10=2 (meaning no ones, but 1 set of 2's); 11=3 (1 set of 1's +1 set of 2's); 100=4 (no ones or twos, but 1 set of 4's); 101=5 (1 set of 1's, no 2's, 1 set of 4's); 110=6; 111=7; 1000=8; 1001=9; and 1010=10. Each space from right side to left is counted as the 1's, 2's, 4's, 6's, 8's, etc. The number 7, for example, is read as 1 set of 1's, 1 set of 2's, 1 set of 4's or 1+2+4=7.

Answer 5

In the counting you have learnt till now, you count in base 10. What that means is you have 10 symbols (0,1,2,...,9) and that everytime you are past one set (in a sense that you will soon understand) of these 10, you jump to the so-called "digit". So that

9+1=10

which is a way of saying 9+1= 1 set of 10 raised to power 1 and 0 of 10 raised to power 0.

Similarly, saym you think of 4789. This is 4 sets of 10 power 3 (that is 1000), 7 of 10 power 2 (100), 8 of 10 power 1 (10) and 9 of 10 power 0 (1).

However keeping 10 symbols is not always convenient, e.g. in computer calculations and you would want to switch to a method of counting that uses on 2 symbols (binary) or even 16 symbols (hexadecimal). The symbols in binary are 0 and 1, while as you may imagine the digits 0-9 fall short of the needs of hexadecimal ("hex") and thus it, in addition 0-9 has, A-F so that the counting in hex goes 0,1,2,3,4,...,8,9,A(10),B(11),C(12),D(13),E(14),F(15).

What do you think will be the next number after F, i.e. 16? To do this, think of decimal (the usual counting). Once you run out of digits you increment the digit to its left and reset this to zero, so 10 in base 16 is next after F.

Similarly in binary, you run out of digits just after 0,1, so what do you do? You say - ok, the next number - let me increment the left position and reset the current one to 0, that is to say, in binary ... 3 is 10.

Hope this helps.

Answer 6

binary is a base 2 number system where all you have are 1 and 0
so
1 = 1
2 = 10
3 = 11
4 = 100

and so on

Answer 7

00 - 0
01 - 1
10 - 2
11 - 3
100 - 4
101 - 5
111 - 6
getting it yet? Seeing a pattern?

Answer 8

it is also a system of 2 stars that revolve around each other...