psp888:
Binary is a number system which determines a digital data. It is made up of 0's and 1's. This system is really a translation of a number in terms of computer. This system is based on all the numbers with the power of 2. Binary always starts with a 1 because the biggest value of 2^x is required 1st. For example, the number 9 has a binary of 1001. There are 4 figure because the biggest number to reach 9 is 2^3. But (2^2)+(2^3) will equal to larger than 9 so the second figure is 0. The thrid figure is also 0 because (2^1)+(2^3) is larger than 9. But (2^0)+(2^3)=9 so the last figure is a 1.
jo3_sum:
Binary was created because computers can read stored data as positively charged ( + ) and negatively charged ( - ) metals; therefore true and false exist a.k.a. 1 and 0. Binary is a very basic way of counting and previously knowing hexadecimal makes it only easier.
Example of binary and its decimal counterpart:
| decimal | binary |
| 0 | 0 |
| 1 | 1 |
| 2 | 10 |
| 3 | 11 |
| 4 | 100 |
| 5 | 101 |
| 6 | 110 |
| 7 | 111 |
| 8 | 1000 |
| 9 | 1001 |
| 10 | 1010 |
| 11 | 1011 |
| 12 | 1100 |
| 13 | 1101 |
| 14 | 1110 |
| 15 | 1111 |
| 16 | 10000 |
| 17 | 10001 |
| 18 | 10010 |
| 19 | 10011 |
| 20 | 10100 |
| 21 | 10101 |
| 22 | 10110 |
| 23 | 10111 |
| 24 | 11000 |
| 25 | 11001 |
| 26 | 11010 |
| 27 | 11011 |
| 28 | 11100 |
| 29 | 11101 |
| 30 | 11110 |
| 31 | 11111 |
| 32 | 100000 |
Theres several things here you may notice. One important thing is just as in the decimal counting system, 1 is less than 10, 10 is than 11, 11 is less than 100, 100 is less than 101, etc. What we can conclude from the above and the previous sentence is that next number must be higher. When counting up in binary, you must count like this:
101→110→111→1000→1001→1010→1011
Notice that 101 is before 110 that is because the next greater number is 110 when only using 1 and 0. But 111 next lowest greater number is 1000, why? Thats because there are no more 0 spaces to fill up with 1's; so like in decimal wen all the spaces are filled with 9's, you must add the next 10's place (i.e. tens, thousands, millions…).
Another important one is that all 2^x (two the power of x) has only one "1". Take a look at 1 (2^0), 2 (2^1), 4 (2^2), 8 (2^3), 16 (2^4)…. Well, you get the point. They all have one "1" which is always followed by zeros except for one,which is 1 (2^0). lol. From this we might test and play with some things and come to a conclusion. For an example, lets look at the number 26. 26 is 11010, so 26 can also be [ 1 * (2^4) + 1 * (2^3) + 0 * (2^2) + 1 * (2^1) + 0 * (2^0)]. Then to ( 1*16 + 1*8 + 0*4 + 1*2 + 0*1). Then, 16 + 8 + 0 + 2 + 0. Then 26! So 26 = 26. But wait, where did i get the one's and zero's from "[1*(2^4)+1*(2^3)+0*(2^2)+1*(2^1)+0*(2^0)]", that's the best part. I got it from here "11010"!!! Heres the steps:
11010 (binary) = 26 (decimal) ???
↓
11010 (binary) = [ 1 * (2^4) + 1 * (2^3) + 0 * (2^2) + 1 * (2^1) + 0 * (2^0)] (decimal)
↓
11010 (binary) = ( 1*16 + 1*8 + 0*4 + 1*2 + 0*1) (decimal)
↓
11010 (binary) = 16 + 8 + 0 + 2 + 0 (decimal)
↓
11010 (binary) = 26 !!!
Talk
psp888 - I found it very hard to clearly explain how binary works. But I hope you can understand it.
MPG - jo3_sum listed this in IM: 0, 1, 10, 11, 100, 101, 110, 111, 1000…….
